Stevo Stević

We give a short proof of the Cushing‐Henson conjecture concerning Beverton‐Holt difference equation, which is important in theoretical ecology. The main result shows that a periodic environment is always deleterious … We give a short proof of the Cushing‐Henson conjecture concerning Beverton‐Holt difference equation, which is important in theoretical ecology. The main result shows that a periodic environment is always deleterious for populations modeled by the Beverton‐Holt difference equation.

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On an integral operator on the unit ball in

2005-01-01

Stevo Stević

Let denote the space of all holomorphic functions on the unit ball . In this paper, we investigate the integral operator , , , where and is the radial derivative … Let denote the space of all holomorphic functions on the unit ball . In this paper, we investigate the integral operator , , , where and is the radial derivative of . The operator can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of the operator on -Bloch spaces is considered.

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ON AN INTEGRAL OPERATOR FROM THE ZYGMUND SPACE TO THE BLOCH-TYPE SPACE ON THE UNIT BALL

2008-12-16

Stevo Stević

Abstract In this paper, we introduce an integral operator on the unit ball $\BB\subset\CC^n$ . The boundedness and compactness of the operator from the Zygmund space to the Bloch-type space … Abstract In this paper, we introduce an integral operator on the unit ball $\BB\subset\CC^n$ . The boundedness and compactness of the operator from the Zygmund space to the Bloch-type space ${\mathcal B}_\mu(\BB)$ or the little Bloch-type space ${\mathcal B}_{\mu,0}(\BB)$ are investigated.

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Global stability and asymptotics of some classes of rational difference equations

2005-05-27

Stevo Stević

Weighted composition operators from Zygmund spaces into Bloch spaces

2008-10-15

Songxiao Li , Stevo Stević

On some solvable systems of difference equations

2011-11-23

Stevo Stević

Products of composition and differentiation operators on the weighted Bergman space

2009-11-01

Stevo Stević

Motivated by a recent paper by S. Ohno we calculate Hilbert-Schmidt norms of products of composition and differentiation operators on the Bergman space $A^2_\alpha,$ $\alpha>-1$ and the Hardy space $H^2$ … Motivated by a recent paper by S. Ohno we calculate Hilbert-Schmidt norms of products of composition and differentiation operators on the Bergman space $A^2_\alpha,$ $\alpha>-1$ and the Hardy space $H^2$ on the unit disk. When the convergence of sequences $(\varphi_n)$ of symbols to a given symbol $\varphi$ implies the convergence of product operators $C_{\varphi_n}D^k$ is also studied. Finally, the boundedness and compactness of the operator $C_{\varphi}D^k: A^2_\alpha\to A^2_\alpha$ are characterized in terms of the generalized Nevanlinna counting function.

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Existence of nontrivial solutions of a rational difference equation

2006-05-09

Stevo Stević

Volterra-Type Operators on Zygmund Spaces

2007-01-01

Songxiao Li , Stevo Stević

The boundedness and the compactness of the two integral operators ; , where is an analytic function on the open unit disk in the complex plane, on the Zygmund space … The boundedness and the compactness of the two integral operators ; , where is an analytic function on the open unit disk in the complex plane, on the Zygmund space are studied.

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Products of integral-type operators and composition operators between Bloch-type spaces

2008-09-14

Songxiao Li , Stevo Stević

On the recursive sequence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:…

2007-09-12

Stevo Stević

Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces

2009-01-30

Stevo Stević

More on a rational recurrence relation.

2004-01-01

Stevo Stević

In this note we give some additional information on the behavior of the solutions of the difference equation xn+1 = xn−1 1 + xn−1xn , n = 0, 1... where … In this note we give some additional information on the behavior of the solutions of the difference equation xn+1 = xn−1 1 + xn−1xn , n = 0, 1... where the initial conditions x−1, x0 are real numbers.

Products of multiplication composition and differentiation operators on weighted Bergman spaces

2011-03-16

Stevo Stević , Ajay K‎. ‎Sharma , Ambika Bhat

On the difference equation xn=xn−2/(bn+cnxn−1xn−2)

2011-11-10

Stevo Stević

Eventually constant solutions of a rational difference equation

2009-05-30

Bratislav Iričanin , Stevo Stević

Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces

2010-08-26

Songxiao Li , Stevo Stević

On the iterated logarithmic Bloch space on the unit ball

2009-01-14

Steven G. Krantz , Stevo Stević

On the difference equation

2011-12-24

Stevo Stević

Norm and essential norm of composition followed by differentiation from -Bloch spaces to

2008-10-27

Stevo Stević

On an integral operator between Bloch-type spaces on the unit ball

2008-11-08

Stevo Stević

Products of composition and integral type operators fromH∞to the Bloch space

2008-04-15

Songxiao Li , Stevo Stević

We study the boundedness and compactness of the products of composition operators and integral type operators from H ∞ to the Bloch space on the unit disk. We study the boundedness and compactness of the products of composition operators and integral type operators from H ∞ to the Bloch space on the unit disk.

On Some Solvable Difference Equations and Systems of Difference Equations

2012-01-01

Stevo Stević , Josef Diblı́k , Bratislav Iričanin +1 more

Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which … Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature.

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On a nonlinear generalized max-type difference equation

2010-11-22

Stevo Stević

On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces

2009-06-27

Stevo Stević

Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences

2014-01-01

Stevo Stević

Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results … Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results in the literature. Some applications concerning a two-dimensional system of bilinear difference equations are also given.

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On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball

2008-09-10

Stevo Stević

Boundedness character of a class of difference equations

2008-01-16

Stevo Stević

Periodicity of a class of nonautonomous max-type difference equations

2011-05-10

Stevo Stević

Composition Operators between H∞ and α-Bloch Spaces on the Polydisc

2006-12-31

Stevo Stević

Let U^n be the unit polydisc of {\mathbb C}^n and \varphi(z)=(\varphi_1(z),\ldots,\varphi_n(z)) a holomorphic self-map of U^n. Let H(U^n) denote the space of all holomorphic functions on U^n, H^\infty(U^n) the space … Let U^n be the unit polydisc of {\mathbb C}^n and \varphi(z)=(\varphi_1(z),\ldots,\varphi_n(z)) a holomorphic self-map of U^n. Let H(U^n) denote the space of all holomorphic functions on U^n, H^\infty(U^n) the space of all bounded holomorphic functions on U^n, and {\cal B}^a(U^n), a>0, the a -Bloch space, i.e., {\cal B}^a(U^n)=\bigg\{ f\in H(U^n)\, |\, \|f\|_{{\cal B}^a}=|f(0)|+\sup\limits_{z\in U^n}\sum\limits^n_{k=1} \left|\frac{\partial f} {\partial z_k}(z)\right|\left(1- |z_k|^2\right)^a<+\infty\bigg\}. \hspace{-0.3cm} We give a necessary and sufficient condition for the composition operator C_{\\varphi} induced by \varphi to be bounded and compact between H^\infty(U^n) and a -Bloch space {\cal B}^a(U^n), when a\geq 1.

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Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces

2011-09-09

Stevo Stević , Ajay K‎. ‎Sharma , Ambika Bhat

On a third-order system of difference equations

2012-02-11

Stevo Stević

Weighted Composition Operators from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E1"><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>∞</mml:mi></mml:msup></mml:mrow></mml:math>to the Bloch Space on the Polydisc

2007-01-01

Songxiao Li , Stevo Stević

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E2"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>be the unit polydisc of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E3"><mml:mrow><mml:msup><mml:mi>ℂ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E4"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>be a holomorphic self-map of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E5"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E6"><mml:mrow><mml:mi>ψ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>a holomorphic function on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E7"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>. Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" … Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E2"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>be the unit polydisc of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E3"><mml:mrow><mml:msup><mml:mi>ℂ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E4"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>be a holomorphic self-map of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E5"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E6"><mml:mrow><mml:mi>ψ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>a holomorphic function on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E7"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>. Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E8"><mml:mrow><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>denote the space of all holomorphic functions with domain<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E9"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E10"><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>∞</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>the space of all bounded holomorphic functions on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E11"><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E12"><mml:mrow><mml:mi mathvariant="fraktur">B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>the Bloch space, that is,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E13"><mml:mrow><mml:mi mathvariant="fraktur">B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>∈</mml:mo><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mrow><mml:mo>‖</mml:mo><mml:mi>f</mml:mi><mml:mo>‖</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mi mathvariant="fraktur">B</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mo>sup</mml:mo></mml:mrow><mml:mrow><mml:mi>z</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:msub><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>∂</mml:mo><mml:mi>f</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo><</mml:mo><mml:mo>+</mml:mo><mml:mi>∞</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>. We give necessary and sufficient conditions for the weighted composition operator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E14"><mml:mrow><mml:mi>ψ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>ϕ</mml:mi></mml:msub></mml:mrow></mml:math>induced by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E15"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E16"><mml:mrow><mml:mi>ψ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>to be bounded and compact from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E17"><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>∞</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>to the Bloch space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E18"><mml:mrow><mml:mi mathvariant="fraktur">B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="double-struck">D</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>.

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Composition followed by differentiation from mixed-norm spaces to α-Bloch spaces

2008-12-31

Songxiao Li , Stevo Stević

In this paper, we study the boundedness and the compactness of products of differentiation operators and composition operators from mixed-norm spaces to α-Bloch spaces. Bibliography: 18 titles. In this paper, we study the boundedness and the compactness of products of differentiation operators and composition operators from mixed-norm spaces to α-Bloch spaces. Bibliography: 18 titles.

Asymptotics of Some Classes of Higher-Order Difference Equations

2007-01-01

Stevo Stević

We present some methods for finding asymptotics of some classes of nonlinear higher-order difference equations. Among others, we confirm a conjecture posed by S. Stević (2005). Monotonous solutions of the … We present some methods for finding asymptotics of some classes of nonlinear higher-order difference equations. Among others, we confirm a conjecture posed by S. Stević (2005). Monotonous solutions of the equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E1"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mstyle displaystyle="true"><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E2"><mml:mrow><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:msub><mml:mi>ℕ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math>, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E3"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>A</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E4"><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℕ</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E5"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>, are natural numbers such that<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E6"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo><</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo><</mml:mo><mml:mo>⋯</mml:mo><mml:mo><</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E7"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mi>∞</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E8"><mml:mrow><mml:mi>j</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E9"><mml:mrow><mml:mstyle displaystyle="true"><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mstyle></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E10"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>s</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E11"><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mo>max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>, are found. A new inclusion theorem is proved. Also, some open problems and conjectures are posed.

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Weighted Composition Operators between Mixed Norm Spaces and Spaces in the Unit Ball

2007-01-01

Stevo Stević

Let be an analytic self-map and let be a fixed analytic function on the open unit ball in . The boundedness and compactness of the weighted composition operator between mixed … Let be an analytic self-map and let be a fixed analytic function on the open unit ball in . The boundedness and compactness of the weighted composition operator between mixed norm spaces and are studied.

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Essential Norms of Weighted Composition Operators from the α‐Bloch Space to a Weighted‐Type Space on the Unit Ball

2008-01-01

Stevo Stević

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator from α ‐Bloch spaces to the weighted‐type space on the unit ball for … This paper finds some lower and upper bounds for the essential norm of the weighted composition operator from α ‐Bloch spaces to the weighted‐type space on the unit ball for the case α ≥ 1.

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Riemann–Stieltjes-type integral operators on the unit ball in

2007-05-24

Songxiao Li , Stevo Stević

Let H(B) denote the space of all holomorphic functions on the unit ball In this article, we investigate the following integral operators f∈ H(B), z∈ B, where g∈ H(B) and … Let H(B) denote the space of all holomorphic functions on the unit ball In this article, we investigate the following integral operators f∈ H(B), z∈ B, where g∈ H(B) and is the radial derivative of h. The operator Tg can be considered as an extension of the Cesàro operator on the unit disk. The boundedness and compactness of the operators Tg and Ig , as well as of the product of the operators between the weighted Bloch spaces are considered.

Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball

2006-01-01

Dana D. Clahane , Stevo Stević

For , let and denote, respectively, the -Bloch and holomorphic -Lipschitz spaces of the open unit ball in . It is known that and are equal as sets when . … For , let and denote, respectively, the -Bloch and holomorphic -Lipschitz spaces of the open unit ball in . It is known that and are equal as sets when . We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator from to .

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Global stability of a difference equation with maximum

2009-01-29

Stevo Stević

On the asymptotics of the difference equation y n (1 + y n − 1 … y n − k + 1) = y n − k

2010-08-02

Lothar Berg , Stevo Stević

We show that the difference equation where , has a positive solution converging to zero, by finding a finite asymptotic expansion of the solution. We also show that if and … We show that the difference equation where , has a positive solution converging to zero, by finding a finite asymptotic expansion of the solution. We also show that if and are arbitrarily given positive numbers, then there exists a solution of the equation such that the subsequences , have partial sums of exponential power series as finite asymptotic expansions. Finally, we sketch the case when q of the limits () are vanishing, where we determine only heuristically the next term of the asymptotic expansion.

On a product-type system of difference equations of second order solvable in closed form

2015-10-12

Stevo Stević , Bratislav Iričanin , Zdeněk Šmarda

It is shown that the following system of difference equations $$z_{n+1}=\frac{z_{n}^{a}}{w_{n-1}^{b}},\qquad w_{n+1}=\frac{w_{n}^{c}}{z_{n-1}^{d}}, \quad n\in \mathbb {N}_{0}, $$ where $a,b,c,d\in \mathbb {Z}$ , $z_{-1}, z_{0}, w_{-1}, w_{0}\in \mathbb {C}$ , is … It is shown that the following system of difference equations $$z_{n+1}=\frac{z_{n}^{a}}{w_{n-1}^{b}},\qquad w_{n+1}=\frac{w_{n}^{c}}{z_{n-1}^{d}}, \quad n\in \mathbb {N}_{0}, $$ where $a,b,c,d\in \mathbb {Z}$ , $z_{-1}, z_{0}, w_{-1}, w_{0}\in \mathbb {C}$ , is solvable in closed form.

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Weighted composition operators from Bergman-type spaces into Bloch spaces

2007-08-01

Songxiao Li , Stevo Stević

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Solvability of a class of nonlinear system of difference equations with homogeneity

2025-05-01

Stevo Stević

Solution to the Problem of Monotonicity of a Class of Sequences Converging to lnp$$ \ln p $$

2025-04-28

Stevo Stević

ABSTRACT We completely describe the monotonicity of the following class of real sequences, , where is a natural number bigger or equal to two and the parameter belongs to the … ABSTRACT We completely describe the monotonicity of the following class of real sequences, , where is a natural number bigger or equal to two and the parameter belongs to the interval , extending and unifying many results in the literature in an elegant way. Here, the monotonicity refers to the monotonicity character of each sequence belonging to the class on the whole domain of indices (i.e., on the set ), not only to the eventual monotonicity of the sequences, which was the case in many previous investigations.

On a special case of a difference equation with powers

2025-01-01

Stevo Stević , Bratislav Iričanin , Witold Kosmala

Investigation of the long-term behaviour of solutions to the nonlinear difference equation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="block"> <a:msub> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mi>A</a:mi> <a:mo>+</a:mo> <a:mfrac> <a:msubsup> <a:mi>x</a:mi> … Investigation of the long-term behaviour of solutions to the nonlinear difference equation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="block"> <a:msub> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mi>A</a:mi> <a:mo>+</a:mo> <a:mfrac> <a:msubsup> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>−</a:mo> <a:mi>m</a:mi> </a:mrow> <a:mi>p</a:mi> </a:msubsup> <a:msubsup> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>−</a:mo> <a:mi>k</a:mi> </a:mrow> <a:mi>r</a:mi> </a:msubsup> </a:mfrac> <a:mo>,</a:mo> <a:mspace width="1em"/> <a:mi>n</a:mi> <a:mo>∈</a:mo> <a:msub> <a:mrow class="MJX-TeXAtom-ORD"> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi mathvariant="double-struck">N</a:mi> </a:mrow> </a:mrow> <a:mn>0</a:mn> </a:msub> <a:mo>,</a:mo> </a:math> where <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>A</j:mi> <j:mo>,</j:mo> <j:mi>p</j:mi> <j:mo>,</j:mo> <j:mi>q</j:mi> <j:mo>∈</j:mo> <j:mrow class="MJX-TeXAtom-ORD"> <j:mrow class="MJX-TeXAtom-ORD"> <j:mi mathvariant="double-struck">R</j:mi> </j:mrow> </j:mrow> </j:math>, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mi>k</n:mi> <n:mo>,</n:mo> <n:mi>m</n:mi> <n:mo>∈</n:mo> <n:msub> <n:mrow class="MJX-TeXAtom-ORD"> <n:mrow class="MJX-TeXAtom-ORD"> <n:mi mathvariant="double-struck">N</n:mi> </n:mrow> </n:mrow> <n:mn>0</n:mn> </n:msub> </n:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mi>k</r:mi> <r:mo>≠</r:mo> <r:mi>m</r:mi> </r:math>, was proposed by S. Stević about twenty years ago. A very special case of the equation (<s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mi>p</s:mi> <s:mo>=</s:mo> <s:mn>1</s:mn> </s:math>, <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mi>r</t:mi> <t:mo>=</t:mo> <t:mn>2</t:mn> </t:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mi>m</u:mi> <u:mo>=</u:mo> <u:mn>0</u:mn> </u:math>) has been recently considered in [J. Appl. Math. Comput. 67(2021), 423–437]. We show that the main results therein are known or have some inaccuracies. Among other things, we show that the boundedness result therein is a consequence of some known results and using one of our previous methods we give a better upper bound for positive solutions to the equation, show that the proof of the global convergence result therein is not correct and provide a complete proof of a generalization, and also show that the results on semi-cycles of positive solutions are not correct and present some correct ones. Several comments are also given and some analyses are conducted.

Convex combinations of some convergent sequences

2024-09-01

Stevo Stević

We consider the convex combinations , of a pair of sequences of real numbers and such that , converging to , and study the location of the limit inside the … We consider the convex combinations , of a pair of sequences of real numbers and such that , converging to , and study the location of the limit inside the intervals , for every or for sufficiently large . We also investigate the same problem for the case of two corresponding sequences converging to . Among other results, we prove some, a bit, unexpected ones. Namely, for each , we determine the exact index at which the sequence changes the monotonicity, and we also determine the type of the monotonicity. A number of interesting remarks are also presented.

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On solvability of a two-dimensional symmetric nonlinear system of difference equations

2024-08-27

Stevo Stević , Bratislav Iričanin , Witold Kosmala +1 more

We show that the system of difference equations $$ x_{n+k}=\frac{x_{n+l}y_{n}-ef}{x_{n+l}+y_{n}-e-f},\quad y_{n+k}= \frac{y_{n+l}x_{n}-ef}{y_{n+l}+x_{n}-e-f},\quad n\in {\mathbb{N}}_{0}, $$ where $k\in {\mathbb{N}}$ , $l\in {\mathbb{N}}_{0}$ , $l< k$ , $e, f\in {\mathbb{C}}$ , and … We show that the system of difference equations $$ x_{n+k}=\frac{x_{n+l}y_{n}-ef}{x_{n+l}+y_{n}-e-f},\quad y_{n+k}= \frac{y_{n+l}x_{n}-ef}{y_{n+l}+x_{n}-e-f},\quad n\in {\mathbb{N}}_{0}, $$ where $k\in {\mathbb{N}}$ , $l\in {\mathbb{N}}_{0}$ , $l< k$ , $e, f\in {\mathbb{C}}$ , and $x_{j}, y_{j}\in {\mathbb{C}}$ , $j=\overline{0,k-1}$ , is theoretically solvable and present some cases of the system when the general solutions can be found in a closed form.

On a nonlinear difference equation of the fourth order solvable in closed form and its solutions

2024-08-27

Stevo Stević

We show that a nonlinear difference equation recently considered in this journal is a special case of a solvable class of nonlinear difference equations and that the difference equation is … We show that a nonlinear difference equation recently considered in this journal is a special case of a solvable class of nonlinear difference equations and that the difference equation is closely related to a difference equation previously considered in the literature. We give some detailed theoretical explanations for the closed-form formulas for the solutions to the four special cases of the difference equation considered therein without giving and theoretical explanations related to them, and also show that several statements on the long-term behaviour of positive solutions to the difference equation are not true.

General solution to a difference equation and the long-term behavior of some of its solutions

2024-04-14

Stevo Stević

Closed-from formulas for the general solution to a difference equation are given, generalizing some special cases in the literature. We also analyze and give some comments on the results on … Closed-from formulas for the general solution to a difference equation are given, generalizing some special cases in the literature. We also analyze and give some comments on the results on the long-term behaviour of some solutions of the special cases.

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Essential norm of linear operators from general weighted‐type spaces to Banach spaces and some applications

2024-02-28

Stevo Stević

We present a result concerning the essential norm of linear operators mapping some general weighted‐type spaces of holomorphic functions on the open unit ball in to Banach spaces. As some … We present a result concerning the essential norm of linear operators mapping some general weighted‐type spaces of holomorphic functions on the open unit ball in to Banach spaces. As some applications, we compare essential norms of a product‐type operator of integral type and a weighted composition operator between some of the general weighted‐type spaces.

Norm of the general polynomial differentiation composition operator from the space of Cauchy transforms to the mth weighted‐type space on the unit disk

2024-01-16

Stevo Stević

We introduce the general polynomial differentiation composition operator where , , , are holomorphic functions on the open unit disk and , , are holomorphic self‐maps of , calculate norm … We introduce the general polynomial differentiation composition operator where , , , are holomorphic functions on the open unit disk and , , are holomorphic self‐maps of , calculate norm of the operator acting from the space of Cauchy transforms to the th weighted‐type space, and characterize its boundedness, as well as the boundedness of the operator acting from the space of Cauchy transforms to the little th weighted‐type space.

Six classes of nonlinear two-dimensional systems of difference equations which are solvable

2024-01-01

Stevo Stević

Symmetric nonlinear solvable system of difference equations

2024-01-01

Stevo Stević , Bratislav Iričanin , Witold Kosmala

We show the theoretical solvability of the system of difference equations <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="block"> <a:msub> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>k</a:mi> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mfrac> <a:mrow> <a:msub> <a:mi>y</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> … We show the theoretical solvability of the system of difference equations <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="block"> <a:msub> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>k</a:mi> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mfrac> <a:mrow> <a:msub> <a:mi>y</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>l</a:mi> </a:mrow> </a:msub> <a:msub> <a:mi>y</a:mi> <a:mi>n</a:mi> </a:msub> <a:mo>−</a:mo> <a:mi>c</a:mi> <a:mi>d</a:mi> </a:mrow> <a:mrow> <a:msub> <a:mi>y</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>l</a:mi> </a:mrow> </a:msub> <a:mo>+</a:mo> <a:msub> <a:mi>y</a:mi> <a:mi>n</a:mi> </a:msub> <a:mo>−</a:mo> <a:mi>c</a:mi> <a:mo>−</a:mo> <a:mi>d</a:mi> </a:mrow> </a:mfrac> <a:mo>,</a:mo> <a:mspace width="1em"/> <a:msub> <a:mi>y</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>k</a:mi> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mfrac> <a:mrow> <a:msub> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>l</a:mi> </a:mrow> </a:msub> <a:msub> <a:mi>x</a:mi> <a:mi>n</a:mi> </a:msub> <a:mo>−</a:mo> <a:mi>c</a:mi> <a:mi>d</a:mi> </a:mrow> <a:mrow> <a:msub> <a:mi>x</a:mi> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi>n</a:mi> <a:mo>+</a:mo> <a:mi>l</a:mi> </a:mrow> </a:msub> <a:mo>+</a:mo> <a:msub> <a:mi>x</a:mi> <a:mi>n</a:mi> </a:msub> <a:mo>−</a:mo> <a:mi>c</a:mi> <a:mo>−</a:mo> <a:mi>d</a:mi> </a:mrow> </a:mfrac> <a:mo>,</a:mo> <a:mspace width="1em"/> <a:mi>n</a:mi> <a:mo>∈</a:mo> <a:msub> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi mathvariant="double-struck">N</a:mi> </a:mrow> <a:mn>0</a:mn> </a:msub> <a:mo>,</a:mo> </a:math> where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> <m:mo>∈</m:mo> <m:mrow class="MJX-TeXAtom-ORD"> <m:mi mathvariant="double-struck">N</m:mi> </m:mrow> </m:math>, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mi>l</p:mi> <p:mo>∈</p:mo> <p:msub> <p:mrow class="MJX-TeXAtom-ORD"> <p:mi mathvariant="double-struck">N</p:mi> </p:mrow> <p:mn>0</p:mn> </p:msub> </p:math>, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mi>l</s:mi> <s:mo><</s:mo> <s:mi>k</s:mi> </s:math>, <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mi>c</t:mi> <t:mo>,</t:mo> <t:mi>d</t:mi> <t:mo>∈</t:mo> <t:mrow class="MJX-TeXAtom-ORD"> <t:mi mathvariant="double-struck">C</t:mi> </t:mrow> </t:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"> <w:msub> <w:mi>x</w:mi> <w:mi>j</w:mi> </w:msub> <w:mo>,</w:mo> <w:msub> <w:mi>y</w:mi> <w:mi>j</w:mi> </w:msub> <w:mo>∈</w:mo> <w:mrow class="MJX-TeXAtom-ORD"> <w:mi mathvariant="double-struck">C</w:mi> </w:mrow> </w:math>, <z:math xmlns:z="http://www.w3.org/1998/Math/MathML"> <z:mi>j</z:mi> <z:mo>=</z:mo> <z:mover> <z:mrow> <z:mn>0</z:mn> <z:mo>,</z:mo> <z:mi>k</z:mi> <z:mo>−</z:mo> <z:mn>1</z:mn> </z:mrow> <z:mo accent="false">¯</z:mo> </z:mover> </z:math>. For several special cases of the system, we give some detailed explanations on how some formulas for their general solutions can be found in closed form, that is, we show their practical solvability. To do this, among other things, we use the theory of homogeneous linear difference equations with constant coefficients and the product-type difference equations with integer exponents, which are theoretically solvable.

Solvability of a nonlinear difference equation of the fifteenth order

2024-01-01

Stevo Stević , Bratislav Iričanin , Witold Kosmala

On compactness of operators from Banach spaces of holomorphic functions to Banach spaces

2024-01-01

Mikael Lindström , David Norrbo , Stevo Stević

Boundedness and Essential Norm of an Operator between Weighted-Type Spaces of Holomorphic Functions on a Unit Ball

2023-09-29

Stevo Stević , Sei-Ichiro Ueki

The boundedness of a sum-type operator between weighted-type spaces is characterized and its essential norm is estimated. The boundedness of a sum-type operator between weighted-type spaces is characterized and its essential norm is estimated.

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Metrical Boundedness and Compactness of a New Operator between Some Spaces of Analytic Functions

2023-08-31

Stevo Stević

The metrical boundedness and metrical compactness of a new operator from the weighted Bergman-Orlicz spaces to the weighted-type spaces and little weighted-type spaces of analytic functions are characterized. The metrical boundedness and metrical compactness of a new operator from the weighted Bergman-Orlicz spaces to the weighted-type spaces and little weighted-type spaces of analytic functions are characterized.

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On a linear operator between weighted‐type spaces of analytic functions

2023-08-30

Stevo Stević , Sei-Ichiro Ueki

We characterize the boundedness, compactness, and estimate essential norm of the polynomial differentiation composition operator between weighted‐type spaces of analytic functions, in terms of the operator symbols and weights. We characterize the boundedness, compactness, and estimate essential norm of the polynomial differentiation composition operator between weighted‐type spaces of analytic functions, in terms of the operator symbols and weights.

Norms of a Product of Integral and Composition Operators between Some Bloch-Type Spaces

2023-05-18

Stevo Stević

We present some formulas for the norm, as well as the essential norm, of a product of composition and an integral operator between some Bloch-type spaces of analytic functions on … We present some formulas for the norm, as well as the essential norm, of a product of composition and an integral operator between some Bloch-type spaces of analytic functions on the unit ball, in terms of given symbols and weights.

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On a Class of Difference Equations with Interlacing Indices of the Fourth Order

2023-03-28

Stevo Stević , Bratislav Iričanin , Witold Kosmala

On some classes of solvable difference equations related to iteration processes

2023-01-01

Stevo Stević

We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations … We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations by presenting methods for constructing them. We also conduct several analyses and give many comments related to the difference equations and iteration processes.

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Polynomial differentiation composition operators from H^p spaces to weighted-type spaces on the unit ball

2023-01-01

Stevo Stević , Sei-Ichiro Ueki

We characterize the boundedness, compactness, and estimate essential norm of a polynomial differentiation composition operator from the Hardy space H p to the weighted-type spaces of holomorphic functions on the … We characterize the boundedness, compactness, and estimate essential norm of a polynomial differentiation composition operator from the Hardy space H p to the weighted-type spaces of holomorphic functions on the unit ball.

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Solvability and representations of the general solutions to some nonlinear difference equations of second order

2023-01-01

Stevo Stević

<abstract>We give detailed theoretical explanations for getting the closed-form formulas and representations for the general solutions to four special cases of a class of nonlinear difference equations of second order … <abstract>We give detailed theoretical explanations for getting the closed-form formulas and representations for the general solutions to four special cases of a class of nonlinear difference equations of second order considered in the literature, present an extension of the class of difference equations which is solvable in closed form, analyze some results on the long-term behavior of the solutions to the class of equations, and give some results on convergence.</abstract>

On a two-dimensional nonlinear system of difference equations close to the bilinear system

2023-01-01

Stevo Stević , Durhasan Turgut Tollu

<abstract>We consider the two-dimensional nonlinear system of difference equations <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ x_n = x_{n-k}\frac{ay_{n-l}+by_{n-(k+l)}}{cy_{n-l}+dy_{n-(k+l)}},\quad y_n = y_{n-k}\frac{{\alpha} x_{n-l}+{\beta} x_{n-(k+l)}}{{\gamma} x_{n-l}+{\delta} x_{n-(k+l)}}, $\end{document} </tex-math></disp-formula> for $ n\in{\mathbb N}_0, … <abstract>We consider the two-dimensional nonlinear system of difference equations <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ x_n = x_{n-k}\frac{ay_{n-l}+by_{n-(k+l)}}{cy_{n-l}+dy_{n-(k+l)}},\quad y_n = y_{n-k}\frac{{\alpha} x_{n-l}+{\beta} x_{n-(k+l)}}{{\gamma} x_{n-l}+{\delta} x_{n-(k+l)}}, $\end{document} </tex-math></disp-formula> for $ n\in{\mathbb N}_0, $ where the delays $ k $ and $ l $ are two natural numbers, and the initial values $ x_{-j}, y_{-j} $, $ 1\le j\le k+l $, and the parameters $ a, b, c, d, {\alpha}, {\beta}, {\gamma}, {\delta} $ are real numbers. We show that the system of difference equations is solvable by presenting a method for finding its general solution in detail. Bearing in mind that the system of equations is a natural generalization of the corresponding one-dimensional difference equation, whose special cases appear in the literature from time to time, our main result presented here also generalizes many results therein.</abstract>

On a family of nonlinear difference equations of the fifth order solvable in closed form

2023-01-01

Stevo Stević , Bratislav Iričanin , Witold Kosmala

<abstract>We present some closed-form formulas for the general solution to the family of difference equations <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ x_{n+1} = \Phi^{-1}\left(\Phi(x_{n-1})\frac{{\alpha} \Phi(x_{n-2})+{\beta} \Phi(x_{n-4})}{{\gamma} \Phi(x_{n-2})+{\delta} \Phi(x_{n-4})}\right), $\end{document} </tex-math></disp-formula> for … <abstract>We present some closed-form formulas for the general solution to the family of difference equations <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ x_{n+1} = \Phi^{-1}\left(\Phi(x_{n-1})\frac{{\alpha} \Phi(x_{n-2})+{\beta} \Phi(x_{n-4})}{{\gamma} \Phi(x_{n-2})+{\delta} \Phi(x_{n-4})}\right), $\end{document} </tex-math></disp-formula> for $ n\in{\mathbb N}_0 $ where the initial values $ x_{-j} $, $ j = \overline{0, 4} $ and the parameters $ {\alpha}, {\beta}, {\gamma} $ and $ {\delta} $ are real numbers satisfying the conditions $ {\alpha}^2+{\beta}^2\ne 0, $ $ {\gamma}^2+{\delta}^2\ne 0 $ and $ \Phi $ is a function which is a homeomorphism of the real line such that $ \Phi(0) = 0, $ generalizing in a natural way some closed-form formulas to the general solutions to some very special cases of the family of difference equations which have been presented recently in the literature. Besides this, we consider in detail some of the recently formulated statements in the literature on the local and global stability of the equilibria as well as on the boundedness character of positive solutions to the special cases of the difference equation and give some comments and results related to the statements.</abstract>

Note on a new class of operators between some spaces of holomorphic functions

2022-12-02

Stevo Stević

<abstract>The boundedness and compactness of a new class of linear operators from the weighted Bergman space to the weighted-type spaces on the unit ball are characterized.</abstract> <abstract>The boundedness and compactness of a new class of linear operators from the weighted Bergman space to the weighted-type spaces on the unit ball are characterized.</abstract>

Norms of some operators between weighted-type spaces and weighted Lebesgue spaces

2022-12-01

Stevo Stević

<abstract>We calculate the norms of several concrete operators, mostly of some integral-type ones between weighted-type spaces of continuous functions on several domains. We also calculate the norm of an integral-type … <abstract>We calculate the norms of several concrete operators, mostly of some integral-type ones between weighted-type spaces of continuous functions on several domains. We also calculate the norm of an integral-type operator on some subspaces of the weighted Lebesgue spaces.</abstract>

On integer parts of the reciprocal remainders of some sums

2022-11-11

Stevo Stević

Abstract We present generalizations of some results on the integer parts of the reciprocal remainders of the zeta function $\zeta (s)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:math> with $s=2$ … Abstract We present generalizations of some results on the integer parts of the reciprocal remainders of the zeta function $\zeta (s)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:math> with $s=2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> and $s=3$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:math> , and a very short and elegant proof of a recent result on the integer parts of the reciprocal remainders of the series $\zeta (3)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:math> . We also give some historical and theoretical remarks to problems of this type, conduct some analyses, and make some connections with the theory of linear difference equations with constant coefficients.

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On a class of recursive relations for calculating square roots of numbers

2022-08-10

Stevo Stević

On a nonlinear second-order difference equation

2022-06-28

Stevo Stević , Bratislav Iričanin , Witold Kosmala +1 more

Abstract We study a nonlinear second-order difference equation which considerably extends some equations in the literature. Our main result shows that the difference equation is solvable in closed form. Some … Abstract We study a nonlinear second-order difference equation which considerably extends some equations in the literature. Our main result shows that the difference equation is solvable in closed form. Some applications of the main result are also given.

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Norm and essential norm of an integral‐type operator from the logarithmic Bloch space to the Bloch‐type space on the unit ball

2022-06-20

Stevo Stević

We calculate norm and essential norm of an integral‐type operator from the logarithmic Bloch space and the little logarithmic Bloch space to Bloch‐type spaces on the unit ball of . … We calculate norm and essential norm of an integral‐type operator from the logarithmic Bloch space and the little logarithmic Bloch space to Bloch‐type spaces on the unit ball of . We show that there is a one‐parameter class of equivalent norms on the logarithmic Bloch space for which the norms can be calculated.

Sum of some product‐type operators from Hardy spaces to weighted‐type spaces on the unit ball

2022-06-15

Stevo Stević , Cheng-shi Huang , Zhijie Jiang

We investigate the boundedness and compactness of the operator , where is the multiplication operator with symbol , which are holomorphic functions on the open unit ball in the composition … We investigate the boundedness and compactness of the operator , where is the multiplication operator with symbol , which are holomorphic functions on the open unit ball in the composition operator with symbol which is a holomorphic self‐map of , and the th iterated radial derivative operator, from the Hardy space to the weighted‐type space on .

Higher order difference equations with homogeneous governing functions nonincreasing in each variable with unbounded solutions

2022-06-13

Stevo Stević , A‎. ‎El-Sayed Ahmed , Bratislav Iričanin +1 more

Abstract By using a comparison method and some difference inequalities we show that the following higher order difference equation $$ x_{n+k}=\frac{1}{f(x_{n+k-1},\ldots ,x_{n})},\quad n\in{\mathbb{N}},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace /><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:math> where $k\in{\mathbb{N}}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi></mml:math> … Abstract By using a comparison method and some difference inequalities we show that the following higher order difference equation $$ x_{n+k}=\frac{1}{f(x_{n+k-1},\ldots ,x_{n})},\quad n\in{\mathbb{N}},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace /><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:math> where $k\in{\mathbb{N}}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi></mml:math> , $f:[0,+\infty )^{k}\to [0,+\infty )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mo>:</mml:mo><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mi>∞</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mi>k</mml:mi></mml:msup><mml:mo>→</mml:mo><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mi>∞</mml:mi><mml:mo>)</mml:mo></mml:math> is a homogeneous function of order strictly bigger than one, which is nondecreasing in each variable and satisfies some additional conditions, has unbounded solutions, presenting a large class of such equations. The class can be used as a useful counterexample in dealing with the boundedness character of solutions to some difference equations. Some analyses related to such equations and a global convergence result are also given.

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Note on difference equations with the right-hand side function nonincreasing in each variable

2022-02-23

Stevo Stević , Bratislav Iričanin , Witold Kosmala +1 more

Abstract We present an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which … Abstract We present an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium. The example shows that the main result in the paper: O. Moaaz, Dynamics of difference equation $x_{n+1}=f(x_{n-l}, x_{n-k})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>x</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:math> (Adv. Differ. Equ. 2018:447, 2018), is incorrect.

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Solvability of thirty-six three-dimensional systems of difference equations of hyperbolic-cotangent type

2022-01-01

Stevo Stević

We present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form. We present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form.

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On a solvable class of nonlinear difference equations of fourth order

2022-01-01

Stevo Stević , Bratislav Iričanin , Witold Kosmala +1 more

We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in … We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of some previously considered very special cases. We also present some applications of the main theorem through two examples, which show that some results in the literature are not correct.

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On a new product-type operator on the unit ball

2022-01-01

Stevo Stević

Let m ∈ N , u j , j = 1,m , be holomorphic functions on the open unit ball B ⊂ C n , ϕ be a holomorphic self-map … Let m ∈ N , u j , j = 1,m , be holomorphic functions on the open unit ball B ⊂ C n , ϕ be a holomorphic self-map of B , and D l be the partial derivative operator in the l th variable l ∈ {1,2,... ,n}.We introduce here the following polynomial differentiation composition operator

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New class of three‐dimensional close‐to‐cyclic systems of difference equations solvable in closed form

2021-12-08

Stevo Stević

We present the following new class of three‐dimensional systems of difference equations where , and show that the systems are solvable in closed form, considerably extending some results in the … We present the following new class of three‐dimensional systems of difference equations where , and show that the systems are solvable in closed form, considerably extending some results in the literature.

Weighted iterated radial composition operators from logarithmic Bloch spaces to weighted‐type spaces on the unit ball

2021-11-21

Stevo Stević , Zhijie Jiang

Let M u be the multiplication operator with symbol u which is a holomorphic function on the open unit ball in the composition operator with symbol φ which is a … Let M u be the multiplication operator with symbol u which is a holomorphic function on the open unit ball in the composition operator with symbol φ which is a holomorphic self‐map of , and , the m th iterated radial derivative operator. The boundedness and compactness of the weighted iterated radial composition operator from logarithmic Bloch spaces to weighted‐type spaces are characterized.

Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class

2021-11-17

Stevo Stević , Bratislav Iričanin , Witold Kosmala +1 more

Abstract There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show … Abstract There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing the hyperbolic-cotangent one. Our analysis shows a bit unexpected fact, namely that the solvability of the class is based on some algebraic relations, not closely related to some trigonometric ones, which enable us to solve them in an elegant way. Some examples of the difference equations belonging to the class which are practically solvable are presented, as well as some interesting comments on connections of the equations with some iteration processes.

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Norm of a multilinear integral operator from product of weighted‐type spaces to weighted‐type space

2021-09-27

Stevo Stević

We investigate the following multilinear integral operator where and is a continuous kernel function satisfying the condition for some functions , which are continuous, increasing, , and a function , … We investigate the following multilinear integral operator where and is a continuous kernel function satisfying the condition for some functions , which are continuous, increasing, , and a function , from a product of weighted‐type spaces to weighted‐type spaces of real functions. We calculate the norm of the operator, extending and complementing some results in the literature. We also give an explanation for a relation between integrals of an L p integrable function and its radialization on .

On a class of difference equations with interlacing indices

2021-06-15

Stevo Stević , A‎. ‎El-Sayed Ahmed , Witold Kosmala +1 more

Abstract Some results on the long-term behavior of solutions to a class of difference equations, which includes numerous nonlinear difference equations of various orders that attracted some attention in the … Abstract Some results on the long-term behavior of solutions to a class of difference equations, which includes numerous nonlinear difference equations of various orders that attracted some attention in the last 15 years, are presented. We also present a natural connection among these difference equations, compare some results on the equations with some other ones in the literature, and give a list of a considerable number of difference equations which can be treated in a similar way.

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Note on a difference equation and some of its relatives

2021-04-13

Stevo Stević , A‎. ‎El-Sayed Ahmed , Witold Kosmala +1 more

We prove an interesting result on convergence of positive solutions to a nonlinear second‐order difference equation of interest to some two‐periodic solutions to the equation, improving a previous result, and … We prove an interesting result on convergence of positive solutions to a nonlinear second‐order difference equation of interest to some two‐periodic solutions to the equation, improving a previous result, and leave an open problem. We also present a method for a unified treatment of closely related nonlinear difference equations, which appear from time to time in the literature.

On a class of solvable difference equations generalizing an iteration process for calculating reciprocals

2021-04-13

Stevo Stević

Abstract The well-known first-order nonlinear difference equation $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:mi>x</mml:mi><mml:msubsup><mml:mi>y</mml:mi><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>,</mml:mo><mml:mspace /><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:math> naturally appeared in the problem of computing the reciprocal value of a given … Abstract The well-known first-order nonlinear difference equation $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:mi>x</mml:mi><mml:msubsup><mml:mi>y</mml:mi><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>,</mml:mo><mml:mspace /><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:math> naturally appeared in the problem of computing the reciprocal value of a given nonzero real number x . One of the interesting features of the difference equation is that it is solvable in closed form. We show that there is a class of theoretically solvable higher-order nonlinear difference equations that include the equation. We also show that some of these equations are also practically solvable.

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Note on constructing a family of solvable sine-type difference equations

2021-04-06

A‎. ‎El-Sayed Ahmed , Bratislav Iričanin , Witold Kosmala +2 more

Abstract We obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations. Abstract We obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations.

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Weighted iterated radial composition operators from weighted Bergman–Orlicz spaces to weighted‐type spaces on the unit ball

2021-03-30

Stevo Stević , Zhijie Jiang

Let be the set of all holomorphic functions on the open unit ball in , φ a holomorphic self‐map of , , and ℜ m the m th iterated radial … Let be the set of all holomorphic functions on the open unit ball in , φ a holomorphic self‐map of , , and ℜ m the m th iterated radial derivative operator on . We characterize the metrical boundedness and metrical compactness of the weighted iterated radial composition operator from the weighted Bergman–Orlicz space to the weighted‐type space.

Note on norm of an m-linear integral-type operator between weighted-type spaces

2021-03-25

Stevo Stević

Abstract We find a necessary and sufficient condition for the boundedness of an m -linear integral-type operator between weighted-type spaces of functions, and calculate norm of the operator, complementing some … Abstract We find a necessary and sufficient condition for the boundedness of an m -linear integral-type operator between weighted-type spaces of functions, and calculate norm of the operator, complementing some results by L. Grafakos and his collaborators. We also present an inequality which explains a detail in the proof of the boundedness of the linear integral-type operator on $L^{p}({\mathbb {R}}^{n})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mo>(</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:math> space.

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Note on norms of two integral‐type operators on some spaces of functions on ℝn

2021-02-20

Stevo Stević

We consider two integral‐type operators, generalizing several classical ones, and calculate their norms on the weighted Lebesgue space , when p ≥ 1 , α > − n , weighted‐type … We consider two integral‐type operators, generalizing several classical ones, and calculate their norms on the weighted Lebesgue space , when p ≥ 1 , α > − n , weighted‐type space , when α > 0 , and space, p ≥ 1 , extending and complementing some results in the literature.

Note on a discrete initial value problem from a competition

2021-01-30

Stevo Stević

Abstract The following discrete initial value problem $$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace /><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:math> $x_{0}=2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> and $x_{1}=5/2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math> , appeared at an international competition. It … Abstract The following discrete initial value problem $$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace /><mml:mi>n</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:math> $x_{0}=2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> and $x_{1}=5/2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math> , appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.

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General solution to subclasses of a two-dimensional class of systems of difference equations

2021-01-01

Stevo Stević

We show practical solvability of the following two-dimensional systems of difference equationswhere u n , v n , w n and s n are x n or y n , … We show practical solvability of the following two-dimensional systems of difference equationswhere u n , v n , w n and s n are x n or y n , by presenting closed-form formulas for their solutions in terms of parameter a, initial values, and some sequences for which there are closed-form formulas in terms of index n.This shows that a recently introduced class of systems of difference equations, contains a subclass such that one of the delays in the systems is equal to four, and that they all are practically solvable, which is a bit unexpected fact.

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A note on general solutions to a hyperbolic-cotangent class of systems of difference equations

2020-12-01

Stevo Stević

Abstract Recently there has been some interest in difference equations and systems whose forms resemble some trigonometric formulas. One of the classes of such systems is the so-called hyperbolic-cotangent class … Abstract Recently there has been some interest in difference equations and systems whose forms resemble some trigonometric formulas. One of the classes of such systems is the so-called hyperbolic-cotangent class of systems of difference equations. The corresponding two-dimensional class has two delays denoted by k and l . So far the class has been studied for the case $k\ne l$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>≠</mml:mo><mml:mi>l</mml:mi></mml:math> , and it was shown that it is practically solvable when $\max \{k,l\}\le 2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>max</mml:mo><mml:mo>{</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi><mml:mo>}</mml:mo><mml:mo>≤</mml:mo><mml:mn>2</mml:mn></mml:math> . In this note we show practical solvability of the system in the case $k=l$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mi>l</mml:mi></mml:math> , not only for small values of k and l , but for all $k=l\in {\mathbb {N}}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mi>l</mml:mi><mml:mo>∈</mml:mo><mml:mi>N</mml:mi></mml:math> , which is the first result of such generality.

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New classes of hyperbolic‐cotangent–type systems of difference equations solvable in closed form

2020-10-22

Stevo Stević

In the case of homogeneous linear difference equations with constant coefficients, only a relatively small part of the equations is practically solvable. This is connected to impossibility to solve all … In the case of homogeneous linear difference equations with constant coefficients, only a relatively small part of the equations is practically solvable. This is connected to impossibility to solve all polynomial equations of degree bigger than four. In the case of nonlinear difference equations and systems the situation is even worse. So it is of interest to find new classes of practically solvable difference equations and systems. Recently, there have been presented several classes of practically solvable hyperbolic‐cotangent–type systems of difference equations. Here, we present a new class of solvable systems of this type. It is a bit surprising that all the systems in the class are practically solvable, especially since several special cases are connected to some polynomials of degree eight.

Coauthor	Papers Together
Bratislav Iričanin	48
Zdeněk Šmarda	35
Songxiao Li	34
Witold Kosmala	27
Kenneth S. Berenhaut	14
Ajay K‎. ‎Sharma	13
Mohammed Alghamdi	11
Josef Diblı́k	10
Sei-Ichiro Ueki	10
Abdullah Alotaibi	9
Lothar Berg	8
Naseer Shahzad	8
John D. Foley	7
Zhijie Jiang	4
Der–Chen Chang	4
A‎. ‎El-Sayed Ahmed	4
Durhasan Turgut Tollu	3
Dana D. Clahane	3
E. M. Elsayed	3
George L. Karakostas	3
Candace M. Kent	3
Martin Böhner	3
Wanping Liu	3
Ze‐Hua Zhou	3
Cengiz Çınar	2
Xiaofan Yang	2
Wan–Tong Li	2
Mikael Lindström	2
Zhi Jiang	2
Benoît F. Sehba	2
Стево Стевич	2
Dalal Adnan Maturi	2
Renyu Chen	2
Ambika Bhat	2
Janusz Brzdȩk	2
Karen Avetisyan	2
Ренью Чен	1
David Norrbo	1
Jennifer E. Dice	1
Leonid Gutnik	1
Сонгсиао Ли	1
Xiaohong Fu	1
Osamu Hatori	1
З Чжоу	1
Pablo Galindo	1
Guang Zhang	1
Zh. Jiang	1
RaviP Agarwal	1
Eva G. Goedhart	1
Xinzhi Liu	1

Invariants and oscillation for systems of two nonlinear difference equations

2001-12-01

G. Papaschinopoulos , C.J. Schinas

On some systems of difference equations

2011-07-25

Lothar Berg , Stevo Stević

On the difference equation xn=xn−2/(bn+cnxn−1xn−2)

2011-11-10

Stevo Stević

On some solvable systems of difference equations

2011-11-23

Stevo Stević

On a System of Two Nonlinear Difference Equations

1998-03-01

G. Papaschinopoulos , C.J. Schinas

Finite Difference Equations

1961-04-01

H. A. Levy , F. Lessman , Herman Feshbach

Generalized composition operators on Zygmund spaces and Bloch type spaces

2007-06-21

Songxiao Li , Stevo Stević

Composition Operators on Spaces of Analytic Functions

2019-03-04

Carl C. Cowen , Barbara D. MacCluer

Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory … Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory in the Ball Norms Boundedness in Classical Spaces on the Disk Compactness and Essential Norms in Classical Spaces on the Disk Hilbert-Schmidt Operators Composition Operators with Closed Range Boundedness on Hp (BN) Small Spaces Compactness on Small Spaces Boundedness on Small Spaces Large Spaces Boundedness on Large Spaces Compactness on Large Spaces Hilbert-Schmidt Operators Special Results for Several Variables Compactness Revisited Wogen's Theorem Spectral Properties Introduction Invertible Operators on the Classical Spaces on the Disk Invertible Operators on the Classical Spaces on the Ball Spectra of Compact Composition Operators Spectra: Boundary Fixed Point, j'(a)

On a nonlinear generalized max-type difference equation

2010-11-22

Stevo Stević

On Some Solvable Difference Equations and Systems of Difference Equations

2012-01-01

Stevo Stević , Josef Diblı́k , Bratislav Iričanin +1 more

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On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball

2009-01-09

Stevo Stević

Norm Of Weighted Composition operators From Bloch Space to H infinity on the Unit Ball.

2008-01-01

Stevo Stević

On a System of Difference Equations

2013-01-01

Özan Ozkan , Abdullah Selçuk Kurbanlı

We have investigated the periodical solutions of the system of rational difference equations , and where . We have investigated the periodical solutions of the system of rational difference equations , and where .

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On Impulsive Beverton-Holt Difference Equations and their Applications

2004-08-01

Leonid Berezansky , Elena Braverman

The asymptotic properties of the impulsive Beverton-Holt difference equation where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients … The asymptotic properties of the impulsive Beverton-Holt difference equation where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients In particular, sufficient extinction and non-extinction conditions are obtained for both equations.

Eventually constant solutions of a rational difference equation

2009-05-30

Bratislav Iričanin , Stevo Stević

On the difference equation

2011-12-24

Stevo Stević

Periodicity of a class of nonautonomous max-type difference equations

2011-05-10

Stevo Stević

On an integral operator on the unit ball in

2005-01-01

Stevo Stević

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On the recursive sequence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:…

2007-09-12

Stevo Stević

On the Recursive Sequencexn+1=α+xn−1/xn

1999-05-01

A. M. Amleh , E.A. Grove , G. Ladas +1 more

Spaces of Holomorphic Functions in the Unit Ball

2005-01-01

Kehe Zhu

Existence of nontrivial solutions of a rational difference equation

2006-05-09

Stevo Stević

On a product-type system of difference equations of second order solvable in closed form

2015-10-12

Stevo Stević , Bratislav Iričanin , Zdeněk Šmarda

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On a k-Order System of Lyness-Type Difference Equations

2007-01-01

G. Papaschinopoulos , C.J. Schinas , G. Stefanidou

We consider the following system of Lyness-type difference equations: , , , , where , , , are positive constants, is an integer, and the initial values are positive real … We consider the following system of Lyness-type difference equations: , , , , where , , , are positive constants, is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system.

On the Asymptotics of Nonlinear Difference Equations

2002-12-31

Lothar Berg

Solutions of nonlinear difference equations of second order are investigated with respect to their asymptotic behaviour. In particular, seven conjectures of Kulenović and Ladas concerning rational difference equations are verified. Solutions of nonlinear difference equations of second order are investigated with respect to their asymptotic behaviour. In particular, seven conjectures of Kulenović and Ladas concerning rational difference equations are verified.

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On positive solutions of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>th order difference equation

2005-09-03

Stevo Stević

Compact composition operators on the Bloch space

1995-01-01

Kevin M. Madigan , Alec Matheson

Necessary and sufficient conditions are given for a composition operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi Baseline f equals f o phi"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> … Necessary and sufficient conditions are given for a composition operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi Baseline f equals f o phi"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:mrow> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>o</mml:mtext> </mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{C_\phi }f = f{\text {o}}\phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to be compact on the Bloch space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {B}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and on the little Bloch space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B 0"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Weakly compact composition operators on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B 0"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are shown to be compact. If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi element-of script upper B 0"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\phi \in {\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a conformal mapping of the unit disk <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper D"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {D}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into itself whose image <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi left-parenthesis double-struck upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\phi (\mathbb {D})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> approaches the unit circle <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper T"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {T}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> only in a finite number of nontangential cusps, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{C_\phi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is compact on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B 0"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. On the other hand if there is a point of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper T intersection phi left-parenthesis double-struck upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> <mml:mo>∩</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {T} \cap \phi (\mathbb {D})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> at which <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi left-parenthesis double-struck upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\phi (\mathbb {D})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> does not have a cusp, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{C_\phi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is not compact.

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A short proof of the Cushing‐Henson conjecture

2006-01-01

Stevo Stević

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On a third-order system of difference equations

2012-02-11

Stevo Stević

On the asymptotics of the difference equation y n (1 + y n − 1 … y n − k + 1) = y n − k

2010-08-02

Lothar Berg , Stevo Stević

Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball

2006-01-01

Dana D. Clahane , Stevo Stević

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Boundedness character of a class of difference equations

2008-01-16

Stevo Stević

Biduals of weighted banach spaces of analytic functions

1993-02-01

Klaus D. Bierstedt , W. H. Summers

Abstract For a positive continuous weight function ν on an open subset G of C N , let Hv ( G ) and Hv 0 ( G ) denote the … Abstract For a positive continuous weight function ν on an open subset G of C N , let Hv ( G ) and Hv 0 ( G ) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that ν f is bounded and ν f vanishes at infinity, respectively. We address the biduality problem as to when Hν ( G ) is naturally isometrically isomorphic to Hν 0 ( G )**, and show in particular that this is the case whenever the closed unit ball in Hν 0 ( G ) in compact-open dense in the closed unit ball of Hν ( G ).

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Composition Operators between H∞ and α-Bloch Spaces on the Polydisc

2006-12-31

Stevo Stević

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On a Third‐Order System of Difference Equations with Variable Coefficients

2012-01-01

Stevo Stević , Josef Diblı́k , Bratislav Iričanin +1 more

We show that the system of three difference equations , , and , n ∈ ℕ 0 , where all elements of the sequences , , , n ∈ ℕ … We show that the system of three difference equations , , and , n ∈ ℕ 0 , where all elements of the sequences , , , n ∈ ℕ 0 , i ∈ {1,2, 3}, and initial values x − j , y − j , z − j , j ∈ {0,1, 2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced.

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Persistence, Oscillatory Behavior, and Periodicity of the Solutions of a System of two Nonlinear Difference Equations

1998-01-01

G. Papaschinopoulos , C.J. Schinas

In this paper we investigate the persistence, the oscillatory behavior and the periodic nature of solutions of a system of two nonlinear difference equations. In this paper we investigate the persistence, the oscillatory behavior and the periodic nature of solutions of a system of two nonlinear difference equations.

ON THE RECURSIVE SEQUENCE $x_{n+1}=x_{n-1}/g(x_n)$

2002-09-01

Stevo Stevi ́c

In [5] the following problem was posed. Is there a solution of the following difference equation $$ x_{n+1}=\displaystyle\frac{\beta x_{n-1}}{\beta+x_n},\quad x_{-1},x_0\gt 0,\ \beta \gt 0, \quad n=0,1,2,... $$ such that $x_n\to … In [5] the following problem was posed. Is there a solution of the following difference equation $$ x_{n+1}=\displaystyle\frac{\beta x_{n-1}}{\beta+x_n},\quad x_{-1},x_0\gt 0,\ \beta \gt 0, \quad n=0,1,2,... $$ such that $x_n\to 0$ as $n\to\infty.$ We prove a result which, as a special case, solves the above problem.

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HARDY–BLOCH TYPE SPACES AND LACUNARY SERIES ON THE POLYDISK

2007-05-01

Karen Avetisyan

Abstract We extend the well-known Paley and Paley-Kahane-Khintchine inequalities on lacunary series to the unit polydisk of $\C^n$ . Then we apply them to obtain sharp estimates for the mean … Abstract We extend the well-known Paley and Paley-Kahane-Khintchine inequalities on lacunary series to the unit polydisk of $\C^n$ . Then we apply them to obtain sharp estimates for the mean growth in weighted spaces h ( p , α), h ( p , log(α)) of Hardy–Bloch type, consisting of functions n -harmonic in the polydisk. These spaces are closely related to the Bloch and mixed norm spaces and naturally arise as images under some fractional operators.

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On the system of difference equations ,

2012-11-24

Stevo Stević

More on a rational recurrence relation.

2004-01-01

Stevo Stević

Note on the bilinear difference equation with a delay

2018-10-22

Stevo Stević , Bratislav Iričanin , Witold Kosmala +1 more

A representation formula for the general solution to a higher‐order rational difference equation has been given recently in this journal. The formula was proved by the method of induction without … A representation formula for the general solution to a higher‐order rational difference equation has been given recently in this journal. The formula was proved by the method of induction without giving any theoretical explanation related to it. Here we show how the corresponding representation formula for the general solution to a general higher‐order rational difference equation, that is, to the bilinear difference equation with a delay, is obtained in an elegant way. We also give some theoretical explanations related to the representation, as well as some explanations related to such types of difference equations. The corresponding representation for a system of bilinear difference equations with delay is also presented.

Solutions of a max-type system of difference equations

2012-04-10

Stevo Stević

Bonded projections, duality, and multipliers in spaces of analytic functions

1971-01-01

A. L. Shields , D. L. Williams

Let $\varphi$ and $\psi$ be positive continuous functions on $[0,1)$ with $\varphi (r) \to 0$ as $r \to 1$ and $\smallint _0^1\psi (r)\;dr < \infty$. Denote by ${A_0}(\varphi )$ and … Let $\varphi$ and $\psi$ be positive continuous functions on $[0,1)$ with $\varphi (r) \to 0$ as $r \to 1$ and $\smallint _0^1\psi (r)\;dr < \infty$. Denote by ${A_0}(\varphi )$ and ${A_\infty }(\varphi )$ the Banach spaces of functions f analytic in the open unit disc D with $|f(z)|\varphi (|z|) = o(1)$ and $|f(z)|\varphi (|z|) = O(1),|z| \to 1$, respectively. In both spaces $\left \|f\right \|_\varphi = {\sup _D}|f(z)|\varphi (|z|)$. Let ${A^1}(\psi )$ denote the space of functions analytic in D with $\left \|f\right \|_\psi = \smallint {\smallint _D}|f(z)|\psi (|z|)\;dx\;dy < \infty$. The spaces ${A_0}(\varphi ),{A^1}(\psi )$, and ${A_\infty }(\varphi )$ are identified in the obvious way with closed subspaces of ${C_0}(D),{L^1}(D)$, and ${L^\infty }(D)$, respectively. For a large class of weight functions $\varphi ,\psi$ which go to zero at least as fast as some power of $(1 - r)$ but no faster than some other power of $(1 - r)$, we exhibit bounded projections from ${C_0}(D)$ onto ${A_0}(\varphi )$, from ${L^1}(D)$ onto ${A^1}(\psi )$, and from ${L^\infty }(D)$ onto ${A_\infty }(\varphi )$. Using these projections, we show that the dual of ${A_0}(\varphi )$ is topologically isomorphic to ${A^1}(\psi )$ for an appropriate, but not unique choice of $\psi$. In addition, ${A_\infty }(\varphi )$ is topologically isomorphic to the dual of ${A^1}(\psi )$. As an application of the above, the coefficient multipliers of ${A_0}(\varphi ),{A^1}(\psi )$, and ${A_\infty }(\varphi )$ are characterized. Finally, we give an example of a weight function pair $\varphi ,\psi$ for which some of the above results fail.

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Invariants for Difference Equations and Systems of Difference Equations of Rational Form

1997-12-01

C.J. Schinas

ON THE RECURSIVE SEQUENCE $x_{n+1}=\displaystyle\frac{A}{\prod^k_{i=0}x_{n-i}}+\displaystyle\frac{1}{\prod^{2(k+1)}_{j=k+2}x_{n-j}}$

2003-01-06

Stevo Stevi ́c

In [6] the authors proposed two open problems concerning the boundedness and the periodic nature of positive solutions of the nonlinear difference equation in the title. In this paper we … In [6] the authors proposed two open problems concerning the boundedness and the periodic nature of positive solutions of the nonlinear difference equation in the title. In this paper we prove a global covergence result and solve the open problems in the case A > 1.

Global stability and asymptotics of some classes of rational difference equations

2005-05-27

Stevo Stević

Global stability of a difference equation with maximum

2009-01-29

Stevo Stević

Products of Volterra type operator and composition operator from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>H</mml:mi><mml:mo>∞</mml:mo></mml:msup></mml:math> and Bloch spaces to Zygmund spaces

2008-04-04

Songxiao Li , Stevo Stević

Weighted Composition Operators from Generalized Weighted Bergman Spaces to Weighted-Type Spaces

2008-01-01

GU Ding-gui

Let be a holomorphic self-map and let be a holomorphic function on the unit ball . The boundedness and compactness of the weighted composition operator from the generalized weighted Bergman … Let be a holomorphic self-map and let be a holomorphic function on the unit ball . The boundedness and compactness of the weighted composition operator from the generalized weighted Bergman space into a class of weighted-type spaces are studied in this paper.

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Invariants for Some Difference Equations

1997-08-01

C.J. Schinas