Sever S Dragomir

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Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula

1998-09-01

Sever S Dragomir , Ravi P. Agarwal

Selected Topics on Hermite-Hadamard Inequalities and Applications

2003-03-01

Sever S Dragomir , Charles Pearce

The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications … The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this monograph we present the basic facts related to Hermite- Hadamard inequalities for convex functions and a large number of results for special means which can naturally be deduced. Hermite-Hadamard type inequalities for other concepts of convexities are also given. The properties of a number of functions and functionals or sequences of functions which can be associated in order to refine the result are pointed out. Recent references that are available online are mentioned as well.

Two mappings in connection to Hadamard's inequalities

1992-06-01

Sever S Dragomir

An inequality of Ostrowski-Grüss' type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules

1997-06-01

Sever S Dragomir , Song Wang

THE HADAMARD INEQUALITIES FOR s-CONVEX FUNCTIONS IN THE SECOND SENSE

1999-01-01

Sever S Dragomir , Simon Fitzpatrick

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On Simpson's inequality and applications

2000-01-01

Sever S Dragomir , Ravi P. Agarwal , Pietro Cerone

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Ostrowski Type Inequalities and Applications in Numerical Integration

2002-01-01

Sever S Dragomir , Themistocles M. Rassias

ON THE HADAMARD’S INEQULALITY FOR CONVEX FUNCTIONS ON THE CO-ORDINATES IN A RECTANGLE FROM THE PLANE

2001-12-01

Sever S Dragomir

An inequality of Hadamard's type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane and some applications are given. An inequality of Hadamard's type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane and some applications are given.

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Applications of Ostrowski's inequality to the estimation of error bounds for some special means and for some numerical quadrature rules

1998-01-01

Sever S Dragomir , Song Wang

ON THE HADAMARD’S INEQULALITY FOR CONVEX FUNCTIONS ON THE CO-ORDINATES IN A RECTANGLE FROM THE PLANE

2001-01-12

Sever S Dragomir

An inequality of Hadamard’s type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane and some applications are given. An inequality of Hadamard’s type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane and some applications are given.

Bounds for the normalised Jensen functional

2006-12-01

Sever S Dragomir

New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and … New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and for complex and real n -tuples are given. Refinements of Shannon's inequality and the positivity of Kullback-Leibler divergence are obtained.

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Ostrowski type inequalities for functions whose derivatives are<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>s</mml:mi></mml:math>-convex in the second sense

2010-05-05

Mohammad W. Alomari , Maslina Darus , Sever S Dragomir +1 more

On the Ostrowski's integral inequality for mappings with bounded variation and applications

2001-01-01

Sever S Dragomir

A generalization of Ostrowski's inequality for mappings with bounded variation and applications in Numerical Analysis for Euler's Beta function is given. A generalization of Ostrowski's inequality for mappings with bounded variation and applications in Numerical Analysis for Euler's Beta function is given.

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A NEW INEQUALITY OF OSTROWSKI'S TYPE IN $L_1$ NORM AND APPLICATIONS TO SOME SPECIAL MEANS AND TO SOME NUMERICAL QUADRATURE RULES

1997-09-01

Sever S Dragomir , Song Wang

In this paper we prove a new Ostrowski's inequality in $L_1$-norm and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules. In this paper we prove a new Ostrowski's inequality in $L_1$-norm and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules.

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On some new inequalities of Hermite-Hadamard type for $m$ -- convex functions

2002-03-31

Sever S Dragomir

Some new inequalities for $m-$convex functions are obtained. Some new inequalities for $m-$convex functions are obtained.

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A Generalization of Grüss's Inequality in Inner Product Spaces and Applications

1999-09-01

Sever S Dragomir

Midpoint-Type Rules from an Inequalities Point of View

2019-06-03

Pietro Cerone , Sever S Dragomir

This paper investigates interior point rules which contain the midpoint as a special case, and obtains explicit bounds through the use of a Peano kernel approach and the modern theory … This paper investigates interior point rules which contain the midpoint as a special case, and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. Thus the simplest open Newton-Cotes rules are examined. Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms. Perturbed quadrature rules are obtained through the use of Grüss, Chebychev and Lupaş inequalities, producing a variety of tighter bounds. The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed. The analysis allows the determination of the partition required that would assure that the accuracy of the result would be within a prescribed error tolerance. It is demonstrated that the bounds of the approximations are equivalent to those obtained from a Peano kernel that produces trapezoidal-type rules.

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Inequalities of Hadamard's Type for Lipschitzian Mappings and Their Applications

2000-05-01

Sever S Dragomir , Y.J. Cho , S.S. Kim

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Inequalities for Beta and Gamma functions via some classical and new integral inequalities

2000-01-01

Sever S Dragomir , Ravi P. Agarwal , NS Barnett

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The Ostrowski's integral inequality for Lipschitzian mappings and applications

1999-12-01

Sever S Dragomir

Quasi-convex functions and Hadamard's inequality

1998-06-01

Sever S Dragomir , C. E. M. Pearce

Some extensions of quasi-convexity appearing in the literature are explored and relations found between them. Hadamard's inequality is connected tenaciously with convexity and versions of it are shown to hold … Some extensions of quasi-convexity appearing in the literature are explored and relations found between them. Hadamard's inequality is connected tenaciously with convexity and versions of it are shown to hold in our setting. Our theorems extend and unify a number of known results. In particular, we derive a generalised Kenyon-Klee theorem.

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A Survey on Cauchy-Bunyakovsky-Schwarz Type Discrete Inequalities

2003-03-01

Sever S Dragomir

The main purpose of this survey is to identify and highlight the discrete inequalities that are connected with (CBS)− inequality and provide refinements and reverse results as well as to … The main purpose of this survey is to identify and highlight the discrete inequalities that are connected with (CBS)− inequality and provide refinements and reverse results as well as to study some functional properties of certain mappings that can be naturally associated with this inequality such as superadditivity, supermultiplicity, the strong versions of these and the corresponding monotonicity properties. Many companion, reverse and related results both for real and complex numbers are also presented.

Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex

2012-10-29

A. Barani , A. G. Ghazanfari , Sever S Dragomir

In this article, we extend some estimates of the right-hand side of a Hermite-Hadamard-type inequality for preinvex functions. Then, a generalization to functions of several variables on invex subsets of … In this article, we extend some estimates of the right-hand side of a Hermite-Hadamard-type inequality for preinvex functions. Then, a generalization to functions of several variables on invex subsets of is introduced.

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Trapezoidal-Type Rules from an Inequalities Point of View

2000-06-27

Pietro Cerone , Sever S Dragomir

The article investigates trapezoid type rules and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities.Both Riemann-Stieltjes and Riemann integrals are evaluated … The article investigates trapezoid type rules and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities.Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms.Perturbed quadrature rules are obtained through the use of Grüss, Chebychev and Lupaş inequalities, producing a variety of tighter bounds.The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed.The analysis allows the determination of the partition required that would assure that the accuracy the result would be within a prescribed error tolerance.

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A new generalization of Ostrowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means

2000-01-01

Sever S Dragomir , Pietro Cerone , John A. Roumeliotis

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Hermite–Hadamard’s type inequalities for operator convex functions

2011-01-29

Sever S Dragomir

New some Hadamard's type inequalities for co-ordinated convex functions

2010-01-01

Mehmet Zeki Sarıkaya , M. Emіn Özdemіr , Sever S Dragomir +1 more

In this paper, we establish new some Hermite-Hadamard's type inequalities of convex functions of 2-variables on the co-ordinates. In this paper, we establish new some Hermite-Hadamard's type inequalities of convex functions of 2-variables on the co-ordinates.

The Ostrowski integral inequality for mappings of bounded variation

1999-12-01

Sever S Dragomir

A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given. A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given.

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Inequalities of Hermite-Hadamard Type for h-Convex Functions on Linear Spaces

2015-12-01

Sever S Dragomir

Some inequalities of Hermite-Hadamard type for h-convex functions defined on convex subsets in real or complex linear spaces are given.Applications for norm inequalities are provided as well. Some inequalities of Hermite-Hadamard type for h-convex functions defined on convex subsets in real or complex linear spaces are given.Applications for norm inequalities are provided as well.

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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

2013-01-01

Sever S Dragomir

SOME OSTROWSKI TYPE INEQUALITIES FOR π-ΤΙΜΕ DIFFERENTIABLE MAPPINGS AND APPLICATIONS

1999-01-01

Pietro Cerone , Sever S Dragomir , John A. Roumeliotis

Some generalizations of the Ostrowski inequality for τι-time differentiable mappings are given.Applications in Numerical Integration and for power series expansions are also presented. Some generalizations of the Ostrowski inequality for τι-time differentiable mappings are given.Applications in Numerical Integration and for power series expansions are also presented.

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On the Hermite-Hadamard Inequality and Other Integral Inequalities Involving Two Functions

2010-01-01

Erhan Set , MEmin Özdemir , Sever S Dragomir

We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary … We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary and based on the use of the Minkowski, Hölder, and Young inequalities.

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Advances in Mathematical Inequalities and Applications

2018-01-01

Praveen Agarwal , Sever S Dragomir , Mohamed Jleli +1 more

Properties of some functionals related to Jensen's inequality

1996-03-01

Sever S Dragomir , Josip ‎Pečarić , Lars‐Erik Persson

Hermite–Hadamard type inequalities for co-ordinated convex and qausi-convex functions and their applications

2019-12-01

Muhammad Amer Latif , Saima Rashid , Sever S Dragomir +1 more

Abstract In the article, we present several Hermite–Hadamard type inequalities for the co-ordinated convex and quasi-convex functions and give an application to the product of the moment of two continuous … Abstract In the article, we present several Hermite–Hadamard type inequalities for the co-ordinated convex and quasi-convex functions and give an application to the product of the moment of two continuous and independent random variables. Our results are generalizations of some earlier results. Additionally, an illustrative example on the probability distribution is given to support our results.

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AN INEQUALITY IMPROVING THE SECOND HERMITE-HADAMARD INEQUALITY FOR CONVEX FUNCTIONS DEFINED ON LINEAR SPACES AND APPLICATIONS FOR SEMI-INNER PRODUCTS

2002-01-01

Sever S Dragomir

An inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the second part of the celebrated Hermite-Hadamard inequality. Applications for … An inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the second part of the celebrated Hermite-Hadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.

AN INEQUALITY OF GRUSS' TYPE FOR RIEMANN-STIELTJES INTEGRAL AND APPLICATIONS FOR SPECIAL MEANS

1998-12-01

Sever S Dragomir , I. A. Fedotov

   In this paper we derive a new inequality ofGruss' type for Riemann-Stieltjes integral and apply it for special means (logarithmic mean, identric mean, etc·. ·).   …    In this paper we derive a new inequality ofGruss' type for Riemann-Stieltjes integral and apply it for special means (logarithmic mean, identric mean, etc·. ·).   

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Inequalities for α-fractional differentiable functions

2017-04-28

Yu–Ming Chu , Muhammad Adil Khan , Tahir Ali +1 more

In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real … In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.

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OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE DERIVATIVES SATISFY CERTAIN CONVEXITY ASSUMPTIONS

2004-04-01

Pietro Cerone , Sever S Dragomir

Ostrowski type inequalities for absolutely continuous functions whose derivatives satisfy certain convexity assumptions are pointed out. Ostrowski type inequalities for absolutely continuous functions whose derivatives satisfy certain convexity assumptions are pointed out.

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Some new Ostrowski-type bounds for the Čebyšev functional and applications

2014-01-01

Pietro Cerone , Sever S Dragomir

Some new inequalities Some new inequalities

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Hermite–Hadamard type inequalities for conformable fractional integrals

2017-06-10

Muhammad Adil Khan , Tahir Ali , Sever S Dragomir +1 more

On some new inequalities for differentiable co-ordinated convex functions

2012-02-15

Muhammad Amer Latif , Sever S Dragomir

Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality for co-ordinated convex functions in … Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality for co-ordinated convex functions in two variables are obtained. Mathematics Subject Classification (2000): 26A51; 26D15

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Ostrowski's Inequality for Monotonous Mappings and Applications

1999-06-01

Sever S Dragomir

An inequality of Ostrowski's type for monotonous nondecreasing mappings is given. Applications for quadrature formulas are pointed out. An inequality of Ostrowski's type for monotonous nondecreasing mappings is given. Applications for quadrature formulas are pointed out.

Operator Inequalities of Ostrowski and Trapezoidal Type

2011-12-07

Sever S Dragomir

New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex

2010-11-23

Mohammad W. Alomari , Maslina Darus , Sever S Dragomir

In this note we obtain some inequalities of Hermite-Hadamardtype for functions whose second derivatives absolute values are quasi-convex.Applications for special means are also provided. In this note we obtain some inequalities of Hermite-Hadamardtype for functions whose second derivatives absolute values are quasi-convex.Applications for special means are also provided.

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Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces

2024-06-11

Sever S Dragomir

Some power inequalities for the numerical radius of a product of two operators in Hilbert spaces with applications for commutators and self-commutators are given. 2000 Mathematics Subject Classification. 47A12, 47A30, … Some power inequalities for the numerical radius of a product of two operators in Hilbert spaces with applications for commutators and self-commutators are given. 2000 Mathematics Subject Classification. 47A12, 47A30, 47A63, 47B15

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Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces

2006-06-23

Sever S Dragomir

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AN INEQUALITY OF OSTROWSKI TYPE FOR MAPPINGS WHOSE SECOND DERIVATIVES ARE BOUNDED AND APPLICATIONS

1999-01-01

Pietro Cerone , Sever S Dragomir , John A. Roumeliotis

ON SIMPSON'S QUADRATURE FORMULA FOR MAPPINGS OF BOUNDED VARIATION AND APPLICATIONS

1999-03-01

Sever S Dragomir

   An estimation of remamder for Simpson's quadrature formula for mappings of bounded variation and applications in theory of special means (logarithmic mean, identric mean, etc ...) are …    An estimation of remamder for Simpson's quadrature formula for mappings of bounded variation and applications in theory of special means (logarithmic mean, identric mean, etc ...) are given.   

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Some refinements of Jensen's inequality

1992-08-01

Sever S Dragomir

Quantum symmetric analysis of interval-valued mappings based on generalized Hukuhara differences

2025-05-29

Muhammad Zakria Javed , Muhammad Uzair Awan , Carmen Elena Stoenoiu +3 more

Lipschitz Type Inequalities for an Integral Transform of Positive Operators With Applications

2025-04-14

Sever S Dragomir

We introduce the following integral transform: \[ D^{(\mu)}(T) := -\int_{0}^{\infty} (\lambda+T)^{-1} d\mu(\lambda), \quad t > 0, \] where $\mu$ is a positive measure on $(0,\infty)$ and the integral is assumed … We introduce the following integral transform: \[ D^{(\mu)}(T) := -\int_{0}^{\infty} (\lambda+T)^{-1} d\mu(\lambda), \quad t > 0, \] where $\mu$ is a positive measure on $(0,\infty)$ and the integral is assumed to exist for $T$ as a positive operator on a complex Hilbert space $H$. In this paper, we show, among other results, that if $ A \geq m_1 > 0 $ and $ B \geq m_2 > 0 $, then: \[ \| D^{(\mu)}(B) - D^{(\mu)}(A) \| \leq \| B - A \|_{[m_1,m_2]} D^{(\mu)}(\cdot), \] where $ D^{(\mu)}(\cdot) $ is a function of $ t $, and $ [m_1,m_2]D^{(\mu)}(\cdot) $ is its divided difference. If $ f: [0,\infty) \to \mathbb{R} $ is an operator monotone function with $ f(0) = 0 $, then: \[ \| f(A)A^{-1} - f(B)B^{-1} \| \leq \| B - A \|_{[m_1,m_2]} f(\cdot)(\cdot)^{-1}. \] Similar inequalities for operator convex functions and some particular examples of interest are also given.

Some Bounds for the Generalized Spherical Numerical Radius of Operator Pairs with Applications

2025-04-05

Najla Altwaijry , Sever S Dragomir , Kais Feki +1 more

This paper investigates a generalization of the spherical numerical radius for a pair (B,C) of bounded linear operators on a complex Hilbert space H. The generalized spherical numerical radius is … This paper investigates a generalization of the spherical numerical radius for a pair (B,C) of bounded linear operators on a complex Hilbert space H. The generalized spherical numerical radius is defined as wp(B,C):=supx∈H,∥x∥=1|⟨Bx,x⟩|p+|⟨Cx,x⟩|p1p, p≥1. We derive lower bounds for wp2(B,C) involving combinations of B and C, where p>1. Additionally, we establish upper bounds in terms of operator norms. Applications include the cases where (B,C)=(A,A*), with A* denoting the adjoint of a bounded linear operator A, and (B,C)=(R(A),I(A)), representing the real and imaginary parts of A, respectively. We also explore applications to the so-called Davis–Wielandt p-radius for p≥1, which serves as a natural generalization of the classical Davis–Wielandt radius for Hilbert-space operators.

Some Hermite-Hadamard Type Inequalities for Convex Functions Defined on Convex Bodies Via Gauss-Ostrogradsky Identity

2025-04-01

Sever S Dragomir

Some Inequalities of Trapezoid Type for Double Integral Mean of Absolutely Continuous Functions

2025-02-01

Sever S Dragomir

Some Applications of a Kittaneh Inequality to Operator-Valued Integrals on Hilbert Spaces

2025-01-21

Sever S Dragomir

Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes

2025-01-14

Abdelghani Lakhdari , Muhammad Uzair Awan , Sever S Dragomir +2 more

Jensen type inequalities for (m,M,ψ)-convex functions with applications

2025-01-01

Sever S Dragomir , S. Ivelić Bra anović , Neda Lovričević

Further norm and numerical radii inequalities for operators involving a positive operator

2025-01-01

Najla Altwaijry , Cristian Conde , Sever S Dragomir +1 more

Inequalities for two power series of noncommutative operators in Hilbert spaces with applications to numerical radius

2025-01-01

Sever S Dragomir , Mübariz Garayev

Tensorial norm inequalities for Taylor's expansions of functions of selfadjoint operators in Hilbert spaces

2025-01-01

Sever S Dragomir , Mübariz Garayev

Majorization-type inequalities for (m, M, ψ)-convex functions with applications

2025-01-01

Sever S Dragomir , Slavica Ivelić Bradanović , Neda Lovričević

Abstract In 2001, S. S. Dragomir introduced a generalized class of convexity, the so-called <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>M</m:mi> <m:mo>,</m:mo> <m:mi>ψ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(m,M,\psi ) … Abstract In 2001, S. S. Dragomir introduced a generalized class of convexity, the so-called <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>M</m:mi> <m:mo>,</m:mo> <m:mi>ψ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(m,M,\psi ) -convex functions, which covers many other classes of convexity. In this article, we prove some useful characterizations of this generalized class of convex functions. We obtain majorization-type inequalities for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>M</m:mi> <m:mo>,</m:mo> <m:mi>ψ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(m,M,\psi ) -convex functions, providing also applications to new estimates for some well-known mean inequalities.

New Bounds for the Euclidean Numerical Radius of Two Operators in Hilbert Spaces

2024-12-24

Najla Altwaijry , Sever S Dragomir , Kais Feki +1 more

This paper presents new weighted lower and upper bounds for the Euclidean numerical radius of pairs of operators in Hilbert spaces. We show that some of these bounds improve on … This paper presents new weighted lower and upper bounds for the Euclidean numerical radius of pairs of operators in Hilbert spaces. We show that some of these bounds improve on recent results in the literature. We also find new inequalities for the numerical radius and the Davis–Wielandt radius. The lower and upper bounds we obtain are not symmetrical.

Some study of the orthogonalities based on double integrals

2024-12-16

Ranran Wang , Qi Liu , Jinyu Xia +1 more

Refinements and Reverses of Some Inequalities for the Normalized Determinants of Sequences of Positive Operators in Hilbert Spaces

2024-12-06

Sever S Dragomir

The author presents several refinements and reverses for the normalized determinant of sequences of operators that have the spectra in a positive interval. For this purpose, the author used some … The author presents several refinements and reverses for the normalized determinant of sequences of operators that have the spectra in a positive interval. For this purpose, the author used some Jensen's type discrete inequalities for twice differentiable functions obtained by the author earlier. Some reverses of the celebrated Ky Fan's inequality for determinants of positive operators are given. Upper and lower bounds in terms of the operator variance are also provided.

New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications

2024-11-14

Sever S Dragomir , Mubariz Tapdigoglu Garayev

Perturbed weighted trapezoid inequalities for convex functions with applications

2024-10-01

Sever S Dragomir , Eder Kikianty

We consider trapezoid type inequalities for twice differentiable convex functions, perturbed by a non-negative weight. Applications on a normed space $ (X, \lVert \,\cdot\, \rVert) $ are considered, by establishing … We consider trapezoid type inequalities for twice differentiable convex functions, perturbed by a non-negative weight. Applications on a normed space $ (X, \lVert \,\cdot\, \rVert) $ are considered, by establishing bounds for the term \[ \begin{multline*} \frac{1}{2} \left[\lVert \frac{x+y}{2} \rVert^p + \frac{\lVert x \rVert^p + \lVert y \rVert^p}{2} \right] - \int_{0}^{1} \lVert (1-t)x + ty \rVert^p \, dt, \\ x, y \in X \end{multline*} \] which can be seen as a combination of both the midpoint and the trapezoid $p$-norm (with $2\leq p<\infty$) inequalities.

On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications

2024-09-30

Muhammad Zakria Javed , Muhammad Uzair Awan , Loredana Ciurdariu +2 more

The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex … The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted quasi-mean, non-negative mapping γ, and center-radius ordering relations to establish a class of extended cr-interval-valued convex stochastic processes. This class yields a combination of innovative convex and non-convex stochastic processes. We characterize our class by illustrating its relationships with other classes as well as certain key attributes and sufficient conditions for this class of processes. Additionally, leveraging Riemann–Liouville stochastic fractional operators and our proposed class, we prove parametric fractional variants of Jensen’s inequality, Hermite–Hadamard’s inequality, Fejer’s inequality, and product Hermite–Hadamard’s like inequality. We establish an interesting relation between means by means of Hermite–Hadamard’s inequality. We utilize the numerical and graphical approaches to showcase the significance and effectiveness of primary findings. Also, the proposed results are powerful tools to evaluate the bounds for stochastic Riemann–Liouville fractional operators in different scenarios for a larger space of processes.

Bounds for operator noncommutative perspectives Via Ostrowski’s inequality

2024-09-27

Sever S Dragomir , Mubariz Tapdigoglu Garayev

An Extension of Left Radau Type Inequalities to Fractal Spaces and Applications

2024-09-23

Bandar Bin‐Mohsin , Abdelghani Lakhdari , Nour El Islem Karabadji +4 more

In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for … In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension μ is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results.

Inequalities for operators and operator pairs in Hilbert spaces

2024-09-13

Najla Altwaijry , Sever S Dragomir , Kais Feki +1 more

Improved Bounds for the Euclidean Numerical Radius of Operator Pairs in Hilbert Spaces

2024-09-12

Najla Altwaijry , Sever S Dragomir , Kais Feki

This paper presents new lower and upper bounds for the Euclidean numerical radius of operator pairs in Hilbert spaces, demonstrating improvements over recent results by other authors. Additionally, we derive … This paper presents new lower and upper bounds for the Euclidean numerical radius of operator pairs in Hilbert spaces, demonstrating improvements over recent results by other authors. Additionally, we derive new inequalities for the numerical radius and the Davis–Wielandt radius as natural consequences of our findings.

Power Bounds for the Numerical Radius of the Off-Diagonal 2 × 2 Operator Matrix

2024-09-12

Najla Altwaijry , Sever S Dragomir , Kais Feki

In this paper, we employ a generalization of the Boas–Bellman inequality for inner products, as developed by Mitrinović–Pečarić–Fink, to derive several upper bounds for the 2p-th power with p≥1 of … In this paper, we employ a generalization of the Boas–Bellman inequality for inner products, as developed by Mitrinović–Pečarić–Fink, to derive several upper bounds for the 2p-th power with p≥1 of the numerical radius of the off-diagonal operator matrix 0AB*0 for any bounded linear operators A and B on a complex Hilbert space H. While the general matrix is not symmetric, a special case arises when B=A*, where the matrix becomes symmetric. This symmetry plays a crucial role in the derivation of our bounds, illustrating the importance of symmetric structures in operator theory.

Lower and Upper Bounds for the Generalized Csiszár f-divergence Operator Mapping

2024-09-05

Sever S Dragomir , Ismail Nikoufar

Tensorial and Hadamard Product Integral Inequalities for Convex Functions of Continuous Fields of Operators in Hilbert Spaces

2024-08-27

Sever S Dragomir

Let H be a Hilbert space and Ω a locally compact Hausdorff space endowed with a Radon measure μ with ∫_{Ω}1dμ(t)=1. In this paper we show among others that, if … Let H be a Hilbert space and Ω a locally compact Hausdorff space endowed with a Radon measure μ with ∫_{Ω}1dμ(t)=1. In this paper we show among others that, if f is continuous differentiable convex on the open interval I, (A_{τ})_{τ∈Ω} is a continuous field of positive operators in B(H) such that Sp(A_{τ}) ⊂I for each τ∈Ω and B and operator such that Sp(B)⊂I, then we have ∫_{Ω}(f′(A_{τ})A_{τ})dμ(τ)⊗1-∫_{Ω}f′(A_{τ})dμ(τ)⊗B ≥∫_{Ω}f(A_{τ})dμ(τ)⊗1-1⊗f(B) ≥(∫_{Ω}A_{τ}dμ(τ)⊗1-(1⊗B))(1⊗f′(B)) and the Hadamard product inequality ∫_{Ω}(f′(A_{τ})A_{τ})dμ(τ)∘1-∫_{Ω}f′(A_{τ})dμ(τ)∘B ≥∫_{Ω}f(A_{τ})dμ(τ)∘1-1∘f(B) ≥∫_{Ω}A_{τ}dμ(τ)∘f′(B)-1∘(f′(B)B).

Inequalities for linear combinations of orthogonal projections and applications

2024-08-26

Najla Altwaijry , Cristian Conde , Sever S Dragomir +1 more

Some Classical Inequalities Associated with Generic Identity and Applications

2024-08-06

Muhammad Zakria Javed , Muhammad Uzair Awan , Bandar Bin‐Mohsin +2 more

In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper … In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski’s inequality, trapezoidal inequality, midpoint inequality, Simpson’s inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of γ and parameter ξ.

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Vector Inequalities for Analytic Functions of Operators in Hilbert Spaces and Applications for Numerical Radius and p-Schatten Norm

2024-08-01

Sever S Dragomir

Some New Grüss’ Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces

2024-06-11

Sever S Dragomir

Some new inequalities of Grüss' type for functions of selfadjoint operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. Several examples for particular functions of interest … Some new inequalities of Grüss' type for functions of selfadjoint operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. Several examples for particular functions of interest are provided as well. 2000 Mathematics Subject Classification. 47A63, 47A99

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Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces

2024-06-11

Sever S Dragomir

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Tensorial Simpson 1/8 Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space

2024-06-10

Vuk Stojiljković , Sever S Dragomir

Several Simpson 1 8 tensorial type inequalities for selfadjoint operators have been obtained with variation depending on the conditions imposed on the function f||1/8[f(A)⊗1 + 6f(A⊗1 + 1⊗B/2) + 1⊗f(B)] … Several Simpson 1 8 tensorial type inequalities for selfadjoint operators have been obtained with variation depending on the conditions imposed on the function f||1/8[f(A)⊗1 + 6f(A⊗1 + 1⊗B/2) + 1⊗f(B)] − ∫01f(λ1⊗B + (1−λ)A⊗1)dλ|| ≤ 5||1⊗B − A⊗1||/32 ||f’||I,+∞.

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New Jensen’s Type Inequalities for Differentiable Log-Convex Functions of Selfadjoint Operators in Hilbert Spaces

2024-06-10

Sever S Dragomir

Some new Jensen's type inequalities for differentiable log-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest … Some new Jensen's type inequalities for differentiable log-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided. 2000 Mathematics Subject Classification. 47A63, 47A99

New Norm Inequalities of Čebyšev Type for Power Series in Banach Algebras

2024-06-04

Sever S Dragomir , MV Boldea , Mihail Megan

Let $f\left( \lambda \right) =\sum_{n=0}^{\infty }\alpha _{n}\lambda ^{n}$ be a function defined by power series with complex coefficients and convergent on the open disk $D\left( 0,R\right) \subset \mathbb{C}$, $R>0$ and … Let $f\left( \lambda \right) =\sum_{n=0}^{\infty }\alpha _{n}\lambda ^{n}$ be a function defined by power series with complex coefficients and convergent on the open disk $D\left( 0,R\right) \subset \mathbb{C}$, $R>0$ and $x,y\in \mathcal{B}$, a Banach algebra, with $xy=yx.$ In this paper we establish some new upper bounds for the norm of the Čebyšev type difference\begin{equation*}f\left( \lambda \right) f\left( \lambda xy\right) -f\left( \lambda x\right)f\left( \lambda y\right)\end{equation*}provide that the complex number $\lambda $ and the vectors $x,y\in \mathcal{B%}$ are such that the series in the above expression are convergent. These results complement the earlier resuls obtained by the authors. Applicationsfor some fundamental functions such as the exponential function and the resolvent function are provided as well.

Tensorial and Hadamard product inequalities of Schwarz type for selfadjoint operators in Hilbert spaces

2024-06-01

Sever S Dragomir

On A -normaloid d -tuples of operators and related questions

2024-05-09

Najla Altwaijry , Sever S Dragomir , Kais Feki

AbstractLet ßA (ℍ) denote the algebra of bounded linear operators on a complex Hilbert space ℍ that admit A-adjoint operators, where A is a non-zero positive semi-definite operator on ℍ. … AbstractLet ßA (ℍ) denote the algebra of bounded linear operators on a complex Hilbert space ℍ that admit A-adjoint operators, where A is a non-zero positive semi-definite operator on ℍ. A commuting operator tuple T = (T1 ,…, Td) ∈ ßA(ℍ)d is called jointly A-normaloid if rA(T) = ∥T∥A, where rA(T) and ∥T∥A represent the joint A-spectral radius and the joint operator A-seminorm of T, respectively. This paper aims to investigate this new class of operators and provides several examples. Furthermore, a characterization of A-normaloidity is established. Additionally, the joint Euclidean A-seminorm of a d-tuple of A-bounded operators T, denoted by , is examined. Specifically, for all positive integers n, we prove that the following equivalence holds for any commuting operator tuple . Here . Finally, several related questions are explored.Mathematics Subject Classification (2020): 47A1247A6347B6546C0547A10Key words: Positive operatorjointly A-normaloid operatorsjoint A-spectral radiusjoint A-numerical radiusjoint A-seminormsjoint approximate A-spectrum

Bullen-Mercer type inequalities with applications in numerical analysis

2024-04-05

Miguel Vivas–Cortez , Muhammad Zakria Javed , Muhammad Uzair Awan +2 more

In mathematical analysis theory of inequalities has considerable influence due to its massive utility in various fields of physical sciences. These are investigated via multiple approaches to acquire more precise … In mathematical analysis theory of inequalities has considerable influence due to its massive utility in various fields of physical sciences. These are investigated via multiple approaches to acquire more precise and rectified forms of already celebrated consequences. Integral inequalities are investigated to compute the error bounds for quadrature schemes. Among all of them, one is Hermite-Hadamard inequality, which has mighty efficacy. Numerous generalizations have been proposed in the literature based on different novel and innovative procedures. In recent years, Bullen inequality has been very commonly studied inequality. The main objective of our progressive study is to establish a new set of Bullen-type inequalities concerning the Jensen-Mecer inequality. For the completion of the current investigation, we derive a new general Bullen-Mecer equality, which is beneficial to achieve our primary consequences. Furthermore, Considering the Bullen-Mecer equation, we employ the convexity property together with famous Hölder's type and Young's inequalities, bounding, and Lipschitz characteristics of functions to conclude new variants of generalized upper bounds of Bullen inequality. Also, we deliver some applications of outcomes to means, special functions, error bounds, and iterative methods to solve non-linear problems. Lastly, we verify our findings through various simulations. The advantage of the current study is that several results concerning Bullen's inequality can be retrieved from our proposed results and various new results can be achieved by choosing the values for γ and δ. By utilizing the similar technique that we have adopted new iterative schemes can be established from integral inequalities.

Some Refinements and Reverses of Callebaut's Inequality for Isotonic Functionals via a Result Due to Cartwright and Field

2024-03-29

Sever S Dragomir

In this paper we obtain some refinements and reverses of Callebaut's inequality for isotonic functionals via a result of Young's inequality due to Cartwright and Field. In this paper we obtain some refinements and reverses of Callebaut's inequality for isotonic functionals via a result of Young's inequality due to Cartwright and Field.

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Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

2024-03-07

Najla Altwaijry , Sever S Dragomir , Kais Feki

The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(λ)=∑k=0∞akλk and … The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(λ)=∑k=0∞akλk and its modified version ha(λ)=∑k=0∞|ak|λk. The convergence of h(λ) is assumed on the open disk D(0,R), where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities.

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Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces

2024-03-06

Najla Altwaijry , Sever S Dragomir , Kais Feki

Consider the power series with complex coefficients h(z)=∑k=0∞akzk and its modified version ha(z)=∑k=0∞|ak|zk. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators … Consider the power series with complex coefficients h(z)=∑k=0∞akzk and its modified version ha(z)=∑k=0∞|ak|zk. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h(z) on the open disk D(0,ρ), where ρ denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.

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Refinements and Reverses of Tensorial and Hadamard Product Inequalities for Selfadjoint Operators in Hilbert Spaces Related to Young's Result

2024-03-01

Sever S Dragomir

Let $H$ be a Hilbert space. In this paper we show among others that, if the selfadjoint operators $A$ and $B$ satisfy the condition $0$ $&lt;$ $m\leq A,$ $B\leq M,$ … Let $H$ be a Hilbert space. In this paper we show among others that, if the selfadjoint operators $A$ and $B$ satisfy the condition $0$ $&lt;$ $m\leq A,$ $B\leq M,$ for some constants $m,$ $M,$ then \begin{align*} 0&amp; \leq \frac{m}{M^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}\otimes 1+1\otimes B^{2}}{2}-A\otimes B\right) \\ &amp; \leq \left( 1-\nu \right) A\otimes 1+\nu 1\otimes B-A^{1-\nu }\otimes B^{\nu } \\ &amp; \leq \frac{M}{m^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}\otimes 1+1\otimes B^{2}}{2}-A\otimes B\right) \end{align*} for all $\nu \in \left[ 0,1\right] .$ We also have the inequalities for Hadamard product \begin{align*} 0&amp; \leq \frac{m}{M^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}+B^{2}}{2}% \circ 1-A\circ B\right) \\ &amp; \leq \left[ \left( 1-\nu \right) A+\nu B\right] \circ 1-A^{1-\nu }\circ B^{\nu } \\ &amp; \leq \frac{M}{m^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}+B^{2}}{2}% \circ 1-A\circ B\right) \end{align*} for all $\nu \in \left[ 0,1\right] .$

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Numerical radius and p-Schatten norm inequalities for power series of operators in Hilbert spaces

2024-02-25

Sever S Dragomir

Let $H$ be a complex Hilbert space. Assume that the power series with complex coefficients $f(z):=\sum\nolimits_{k=0}^{\infty }a_{k}z^{k}$ is convergent on the open disk $D(0,R),~f_{a}(z):=\sum\nolimits_{k=0}^{\infty}\left\vert a_{k}\right\vert z^{k}$ that has the same … Let $H$ be a complex Hilbert space. Assume that the power series with complex coefficients $f(z):=\sum\nolimits_{k=0}^{\infty }a_{k}z^{k}$ is convergent on the open disk $D(0,R),~f_{a}(z):=\sum\nolimits_{k=0}^{\infty}\left\vert a_{k}\right\vert z^{k}$ that has the same radius of convergence $R$ and $A,~B,~C\in B(H)$ with $\left\Vert A\right\Vert $ &lt;$R$, then we have the following Schwarz type inequality $ \left\vert \left\langle C^{\ast }Af(A)Bx,y\right\rangle \right\vert \leq f_{a}(\left\Vert A\right\Vert )\left\langle \left\vert \left\vert A\right\vert ^{\alpha }B\right\vert ^{2}x,x\right\rangle ^{1/2}\left\langle \left\vert \left\vert A^{\ast }\right\vert ^{1-\alpha }C\right\vert ^{2}y,y\right\rangle ^{1/2} $ for $\alpha \in \lbrack 0,1]$ and $x,y\in H.$ Some natural applications for numerical radius and p-Schatten norm are also provided.

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Refinement of the Cauchy-Schwartz inequality with refinements and generalizations of the numerical radius type inequalities for operators

2024-02-17

Vuk Stojiljković , Sever S Dragomir

Motivated by the results previously reported, the current work aims at developing new numerical radius upper bounds of Hilbert space opera- tors by offering new improvements to the well-known Cauchy-Schwarz … Motivated by the results previously reported, the current work aims at developing new numerical radius upper bounds of Hilbert space opera- tors by offering new improvements to the well-known Cauchy-Schwarz inequal- ity. In particular, a novel Lemma (3.1) is given, which is utilized to further generalize several vector and numerical radius type inequalities, as well as pre- viously given extensions of the Cauchy-Schwartz inequality. Specifically, (2.5) (2.8) (1.6) have been generalized by (4.3) (4.1) (4.2)

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Properties and Applications of Symmetric Quantum Calculus

2024-02-12

Miguel Vivas–Cortez , Muhammad Zakria Javed , Muhammad Uzair Awan +2 more

Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. … Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young’s inequality, Hölder’s inequality, Minkowski’s inequality, Hermite–Hadamard’s inequality, Ostrowski’s inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard’s inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals.

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Optical soliton solutions of fokas system and (2 + 1) Davey-Stewartson system by mapping method

2024-01-25

Naveed Ahmed , Mehwish Rani , Sever S Dragomir +1 more

Abstract In this article, a very effective technique called generalized auxiliary equation mapping method has been employed to investigate some very important nonlinear equations in optical fibers such as Fokas … Abstract In this article, a very effective technique called generalized auxiliary equation mapping method has been employed to investigate some very important nonlinear equations in optical fibers such as Fokas system and <?CDATA $(2+1)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> Davey-Stewartson (DS) system. Under different situations, the obtained solutions exhibit various wave pattern like bright and dark soliton, kink soliton, periodic wave soliton and singular solitons. These solutions are novel and interesting and prove the efficiency of the method. The accuracy of the obtained results provides the competence of the method and ensures that it can be used for other mathematical models involved in optical fibers. Graphical simulation of some reported results has been discussed here to visualize and support the mathematical results in terms of 3D, 2D and contour plots.

Upper bounds for the Euclidean spectral radius of operators via joint norms

2024-01-10

Najla Altwaijry , Sever S Dragomir , Kais Feki

Let re(S) be the Euclidean spectral radius associated with a q-tuple S=(S1,…,Sq) of bounded linear operators on a complex Hilbert space. The principal objective of our study is to establish … Let re(S) be the Euclidean spectral radius associated with a q-tuple S=(S1,…,Sq) of bounded linear operators on a complex Hilbert space. The principal objective of our study is to establish various compelling upper bounds involving re(⋅). In particular, our findings demonstrate that, for all t∈[0,1], we have re(S)≤12max{ω(S),ω(Δt(S))}+12‖S‖12‖S‖e12.Here, Δt(S) represents the generalized spherical Aluthge transform of S, while the notations ω(⋅), ‖⋅‖, and ‖⋅‖e pertain to the joint numerical radius, joint operator norm, and Euclidean operator norm, respectively, of operators in Hilbert spaces. Furthermore, we extend the notions of spherical and Duggal transforms and derive multiple upper bounds for re(S) in relation to these transforms. Additionally, there are some applications that are derived as well.

An Ostrowski Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

2024-01-08

Sever S Dragomir

Let H be a Hilbert space. Assume that f is continuously differentiable on I with ‖f′‖_{I,∞}:=sup_{t∈I}|f′(t)| Let H be a Hilbert space. Assume that f is continuously differentiable on I with ‖f′‖_{I,∞}:=sup_{t∈I}|f′(t)|

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Some New f-Divergence Measures and Their Basic Properties

2024-01-04

Sever S Dragomir

In this paper we introduce some new f-divergence measures that we call t-asymmetric/symmetric divergence measure and integral divergence measure, establish their joint convexity and provide some inequalities that connect these … In this paper we introduce some new f-divergence measures that we call t-asymmetric/symmetric divergence measure and integral divergence measure, establish their joint convexity and provide some inequalities that connect these f-divergences to the classical one intyroduced by Csiszar in 1963. Applications for the dichotomy class of convex functions are provided as well.

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On Fejér-type inequalities for generalized trigonometrically and hyperbolic k-convex functions

2024-01-01

Sever S Dragomir , Mohamed Jleli , Bessem Samet

Abstract For <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>I</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \mu \in {C}^{1}\left(I) , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>></m:mo> … Abstract For <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>I</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \mu \in {C}^{1}\left(I) , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> \mu \gt 0 , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>∈</m:mo> <m:mi>C</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>I</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \lambda \in C\left(I) , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>I</m:mi> </m:math> I is an open interval of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="double-struck">R</m:mi> </m:math> {\mathbb{R}} , we consider the set of functions <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>f</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>I</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> f\in {C}^{2}\left(I) satisfying the second-order differential inequality <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfrac> <m:mrow> <m:mi mathvariant="normal">d</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant="normal">d</m:mi> <m:mi>t</m:mi> </m:mrow> </m:mfrac> <m:mfenced open="(" close=")"> <m:mrow> <m:mi>μ</m:mi> <m:mfrac> <m:mrow> <m:mi mathvariant="normal">d</m:mi> <m:mi>f</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant="normal">d</m:mi> <m:mi>t</m:mi> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> <m:mo>+</m:mo> <m:mi>λ</m:mi> <m:mi>f</m:mi> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:math> \frac{{\rm{d}}}{{\rm{d}}t}\left(\phantom{\rule[-0.75em]{}{0ex}},\mu \frac{{\rm{d}}f}{{\rm{d}}t}\right)+\lambda f\ge 0 in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>I</m:mi> </m:math> I . The considered set includes several classes of generalized convex functions from the literature. In particular, if <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>≡</m:mo> <m:mn>1</m:mn> </m:math> \mu \equiv 1 and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>=</m:mo> <m:msup> <m:mrow> <m:mi>k</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> \lambda ={k}^{2} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> k\gt 0 , we obtain the class of trigonometrically <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> </m:math> k -convex functions, while if <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> <m:mo>≡</m:mo> <m:mn>1</m:mn> </m:math> \mu \equiv 1 and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>=</m:mo> <m:mo>−</m:mo> <m:msup> <m:mrow> <m:mi>k</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> \lambda =-{k}^{2} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> k\gt 0 , we obtain the class of hyperbolic <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> </m:math> k -convex functions. In this article, we establish a Fejér-type inequality for the introduced set of functions without any symmetry condition imposed on the weight function and discuss some special cases of weight functions. Moreover, we provide characterizations of the classes of trigonometrically and hyperbolic <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> </m:math> k -convex functions.

Reverse Ostrowski's type weighted inequalities for convex functions on linear spaces with applications

2024-01-01

Sever S Dragomir , Mohamed Jleli , Bessem Samet

Operator upper bounds for Davis-Choi-Jensen's difference in Hilbert spaces

2024-01-01

Sever S Dragomir

In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference Ph (f (A)) - f (Ph (A)) for any convex function f : I → … In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference Ph (f (A)) - f (Ph (A)) for any convex function f : I → R, any selfadjoint operator A in H with the spectrum Sp (A) ⊂ I and any linear, positive and normalized map Ph : B (H) → B (K), where H and K are Hilbert spaces. Some examples of convex and operator convex functions are also provided.

Coauthor	Papers Together
Pietro Cerone	85
Neil S Barnett	40
Muhammad Amer Latif	26
Najla Altwaijry	20
Kais Feki	20
Eder Kikianty	19
Anthony Sofo	17
Kuei-Lin Tseng	17
Mohammad Sal Moslehian	14
E. Momoniat	14
C Buse	14
John A. Roumeliotis	13
Yeol Je Cho	11
C. E. M. Pearce	11
M. Rostamian Delavar	11
Josip ‎Pečarić	11
Young-Ho Kim	10
Muhammad Uzair Awan	9
Seong-Sik Kim	8
Shiow-Ru Hwang	8
Pintu Bhunia	8
Kallol Paul	8
Alawiah Ibrahim	7
Ravi P. Agarwal	7
N. S. Barnett	7
Feng Qi	7
Mehwish Rani	6
Vahid Darvish	6
Naveed Ahmed	6
Mohammad W. Alomari	6
Nicoleta Dragomir	6
Ian Gomm	6
Haji Mohammad Nazari	6
Ali Taghavi	6
B. Mond	6
Maslina Darus	6
Zaki Mrzog Alaofi	5
Y.J. Cho	5
Wing‐Sum Cheung	5
Mohammad Masjed‐Jamei	5
Erhan Set	5
József Sándor	5
Muhammad Zakria Javed	5
Ather Qayyum	4
Ravi P. Agarwal	4
G.-S. Yang	4
Cristian Conde	4
Imran Abbas Baloch	4
Manuel De la Sen	4
Nicoleta M. Ionescu	4

Classical and new inequalities in analysis

1993-12-01

D. S. Mitrinović , J. E. Pečarić , A. M. Fink

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Applications of Ostrowski's inequality to the estimation of error bounds for some special means and for some numerical quadrature rules

1998-01-01

Sever S Dragomir , Song Wang

Classical and New Inequalities in Analysis

1993-01-01

D. S. Mitrinović , Josip ‎Pečarić , A. M. Fink

An inequality of Ostrowski-Grüss' type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules

1997-06-01

Sever S Dragomir , Song Wang

Ostrowski Type Inequalities and Applications in Numerical Integration

2002-01-01

Sever S Dragomir , Themistocles M. Rassias

A NEW INEQUALITY OF OSTROWSKI'S TYPE IN $L_1$ NORM AND APPLICATIONS TO SOME SPECIAL MEANS AND TO SOME NUMERICAL QUADRATURE RULES

1997-09-01

Sever S Dragomir , Song Wang

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�ber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert

1937-12-01

Alexander Ostrowski

Selected Topics on Hermite-Hadamard Inequalities and Applications

2003-03-01

Sever S Dragomir , Charles Pearce

The Ostrowski's integral inequality for Lipschitzian mappings and applications

1999-12-01

Sever S Dragomir

Midpoint-Type Rules from an Inequalities Point of View

2019-06-03

Pietro Cerone , Sever S Dragomir

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AN INEQUALITY IMPROVING THE SECOND HERMITE-HADAMARD INEQUALITY FOR CONVEX FUNCTIONS DEFINED ON LINEAR SPACES AND APPLICATIONS FOR SEMI-INNER PRODUCTS

2002-01-01

Sever S Dragomir

Bounds for the normalised Jensen functional

2006-12-01

Sever S Dragomir

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A Generalization of Grüss's Inequality in Inner Product Spaces and Applications

1999-09-01

Sever S Dragomir

On the Ostrowski's integral inequality for mappings with bounded variation and applications

2001-01-01

Sever S Dragomir

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Convex Functions, Partial Orderings, and Statistical Applications

1992-01-01

Josip ‎Pečarić , Frank Proschan , Y. L. Tong

Ostrowski's Inequality for Monotonous Mappings and Applications

1999-06-01

Sever S Dragomir

Two mappings in connection to Hadamard's inequalities

1992-06-01

Sever S Dragomir

Univariate Ostrowski Inequalities, Revisited

2002-04-01

George A. Anastassiou

AN INEQUALITY OF GRUSS' TYPE FOR RIEMANN-STIELTJES INTEGRAL AND APPLICATIONS FOR SPECIAL MEANS

1998-12-01

Sever S Dragomir , I. A. Fedotov

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The Ostrowski integral inequality for mappings of bounded variation

1999-12-01

Sever S Dragomir

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Operator Inequalities of Ostrowski and Trapezoidal Type

2011-12-07

Sever S Dragomir

SOME OSTROWSKI TYPE INEQUALITIES FOR π-ΤΙΜΕ DIFFERENTIABLE MAPPINGS AND APPLICATIONS

1999-01-01

Pietro Cerone , Sever S Dragomir , John A. Roumeliotis

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Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula

1998-09-01

Sever S Dragomir , Ravi P. Agarwal

Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces

2003-01-01

Sever S Dragomir

The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities … The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or complex inner product spaces are presented as well. Generalizations of the Boas-Bellman, Bombieri, Selberg, Heilbronn and Pecaric inequalities for finite sequences of vectors that are not necessarily orthogonal are also provided. Two extensions of the celebrated Ostrowski's inequalities for sequences or real numbers and the generalization of Wagner's inequality in inner product spaces are pointed out. Finally, some Gruss type inequalities for n-tuples of vectors in inner product spaces and their natural applications for the approximation of the discrete Fourier and Mellin transforms are given as well.

An Ostrowski like inequality for convex functions and applications

2003-01-01

Sever S Dragomir

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Čebyšev's type inequalities for functions of selfadjoint operators in Hilbert spaces

2009-11-06

Sever S Dragomir

Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given.

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Hermite and convexity

1985-12-01

D. S. Mitrinović , Igor Lacković

Bounds on the deviation of a function from its averages

1992-01-01

A. M. Fink

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P-functions, Quasi-convex Functions, and Hadamard-type Inequalities

1999-12-01

C. E. M. Pearce , A. M. Rubinov

ON THE OSTROWSKI INEQUALITY FOR THE RIEMANN-STIELTJES INTEGRAL F a b f (t) du (t) ; WHERE f IS OF HÖLDER TYPE AND u IS OF BOUNDED VARIATION AND APPLICATIONS

2001-06-01

Sever S Dragomir

Some Gruss Type Inequalities in Inner Product Spaces

2003-02-21

Sever S Dragomir

Some new Gruss type inequalities in inner product spaces and applications for integrals are given. Some new Gruss type inequalities in inner product spaces and applications for integrals are given.

On some Hadamard-type inequalities for h-convex functions

2008-01-01

Mehmet Zeki Sarıkaya , Aziz Sağlam , Hüseyin Yıldırım

In this paper, some inequalities Hadamard-type for h -convex functions are given.We also proved some Hadamard-type inequalities for products of two h -convex functions. In this paper, some inequalities Hadamard-type for h -convex functions are given.We also proved some Hadamard-type inequalities for products of two h -convex functions.

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THE HADAMARD INEQUALITIES FOR s-CONVEX FUNCTIONS IN THE SECOND SENSE

1999-01-01

Sever S Dragomir , Simon Fitzpatrick

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Some remarks ons-convex functions

1994-08-01

Henryk Hudzik , Lech Maligranda

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Quasi-convex functions and Hadamard's inequality

1998-06-01

Sever S Dragomir , C. E. M. Pearce

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A variant of Jensen’s inequality of Mercer’s type for operators with applications

2006-05-05

Anita Matković , Josip ‎Pečarić , I‎. ‎Perić

Hermite-Hadamard's inequality and the p-HH-norm on the Cartesian product of two copies of a normed space

2010-01-01

Eder Kikianty , Sever S Dragomir

The Cartesian product of two copies of a normed space is naturally equipped with the well-known p -norm.In this paper, another notion of norm is introduced, and will be called … The Cartesian product of two copies of a normed space is naturally equipped with the well-known p -norm.In this paper, another notion of norm is introduced, and will be called the p -HH -norm.This norm is an extension of the generalised logarithmic mean and is connected to the p -norm by the Hermite-Hadamard's inequality.The Cartesian product space (with respect to both norms) is complete, when the (original) normed space is.A proof for the completeness of the p -HH -norm via Ostrowski's inequality is provided.This space is embedded as a subspace of the well-known Lebesgue-Bochner function space (as a closed subspace, when the norm is a Banach norm).Consequently, its geometrical properties are inherited from those of Lebesgue-Bochner space.An explicit expression of the superior (inferior) semi-inner product associated to both norms is considered and used to provide alternative proofs for the smoothness and reflexivity of this space.

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Ostrowski type inequalities for isotonic linear functionals.

2002-01-01

Sever S Dragomir

A NOTE ON THE PERTURBED TRAPEZOID INEQUALITY

2002-01-01

Xiaoliang Cheng , Jie Sun

In this paper, we utilize a variant of the Gruss inequality to obtain some new per- turbed trapezoid inequalities. We improve the error bound of the trapezoid rule in numerical … In this paper, we utilize a variant of the Gruss inequality to obtain some new per- turbed trapezoid inequalities. We improve the error bound of the trapezoid rule in numerical integration in some recent known results. Also we give a new Iyengar's type inequality involv- ing a second order bounded derivative for the perturbed trapezoid inequality.

Introduction to Spectral Theory in Hilbert Space

1969-01-01

Gilbert Helmberg

Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

2013-01-01

Sever S Dragomir

REVERSES OF SCHWARZ, TRIANGLE AND BESSEL INEQUALITIES IN INNER PRODUCT SPACES

2004-01-01

Sever S Dragomir

Reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in … Reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for integral inequalities are also pointed out.

Trapezoidal-Type Rules from an Inequalities Point of View

2000-06-27

Pietro Cerone , Sever S Dragomir

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Hadamard-type inequalities for s-convex functions

2007-03-19

U.S. Kirmaci , Milica Klaričić Bakula , M. Emіn Özdemіr +1 more

Information-type measures of difference of probability distributions and indirect observation

1967-01-01

Imre Csiszár

On h-convexity

2006-04-06

Sanja Varošanec

Properties of some functionals related to Jensen's inequality

1996-03-01

Sever S Dragomir , Josip ‎Pečarić , Lars‐Erik Persson

Inequalities Involving Functions and Their Integrals and Derivatives

1991-01-01

D. S. Mitrinović , Josip ‎Pečarić , A. M. Fink

NEW VERSIONS OF REVERSE YOUNG AND HEINZ MEAN INEQUALITIES WITH THE KANTOROVICH CONSTANT

2015-03-01

Wenshi Liao , Junliang Wu , Jianguo Zhao

We show new versions of reverse Young inequalities by virtue of the Kantorovich constant, and utilizing the new reverse Young inequalities we give the reverses of the weighted arithmetic-geometric and … We show new versions of reverse Young inequalities by virtue of the Kantorovich constant, and utilizing the new reverse Young inequalities we give the reverses of the weighted arithmetic-geometric and geometric-harmonic mean inequalities for two positive operators. Also, new versions of reverse Young and Heinz mean inequalities for unitarily invariant norms are established.

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A Generalized Trapezoid Inequality for Functions of Bounded Variation

2000-11-07

Pietro Cerone , Sever S Dragomir , C. E. M. Pearce

We establish a generalization of a recent trapezoid inequality for functions of bounded variation. A number of special cases are considered. Applications are made to quadrature formulae, probability theory, special … We establish a generalization of a recent trapezoid inequality for functions of bounded variation. A number of special cases are considered. Applications are made to quadrature formulae, probability theory, special means and the estimation of the beta function.