In the present manuscript, we define a non-negative parametric variant of BaskakovâDurrmeyer operators to study the convergence of Lebesgue measurable functions and introduce these as α-BaskakovâDurrmeyer operators. We study the âŠ
In the present manuscript, we define a non-negative parametric variant of BaskakovâDurrmeyer operators to study the convergence of Lebesgue measurable functions and introduce these as α-BaskakovâDurrmeyer operators. We study the uniform convergence of these operators in weighted spaces.
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators.Modulus of continuity, second modulus of continuity, âŠ
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators.Modulus of continuity, second modulus of continuity, Peeter's K-functional, weighted modulus of continuity and Lipschitz class are considered to prove our results.
The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of SzĂĄsz type operators known as Phillips operators. To âŠ
The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of SzĂĄsz type operators known as Phillips operators. To achieve the results of a better way of uniform convergence of the Phillips operators, we study qualitative results in a Korovkin and weighted Korovkin space.
<p style='text-indent:20px;'>The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a} $\end{document}</tex-math></inline-formula>sz-Schurer-Beta type operators to approximate a class of Lebesgue âŠ
<p style='text-indent:20px;'>The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a} $\end{document}</tex-math></inline-formula>sz-Schurer-Beta type operators to approximate a class of Lebesgue integrable functions. Moreover, we calculate basic estimates and central moments for these sequences of operators. Further, rapidity of convergence and order of approximation are investigated in terms of Korovkin theorem and modulus of smoothess. In subsequent section, local and global approximation properties are studied in various functional spaces.</p>
In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. âŠ
In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. In the last, we prove weighted approximation results.
The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence âŠ
The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre?s K-functional, Lipschitz type class.
The goal of this research article is to introduce a sequence of αâStancuâSchurerâKantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of âŠ
The goal of this research article is to introduce a sequence of αâStancuâSchurerâKantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional αâStancuâSchurerâKantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented.
The main purpose of this article is to study the bivariate approximation generalization for Baskakov-Durrmeyer-operators with the aid of non-negative parametric variants suppose 0 ? ?1,?2 ? 1. We obtain âŠ
The main purpose of this article is to study the bivariate approximation generalization for Baskakov-Durrmeyer-operators with the aid of non-negative parametric variants suppose 0 ? ?1,?2 ? 1. We obtain the order of approximation by use of the modulus of continuity in terms of well known Peetre?s K-functional, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in B?gel-spaces by use of mixed-modulus of continuity.
Abstract In this article, we introduce generalized beta extension of Sz $$\acute{a}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>a</mml:mi><mml:mo>ÂŽ</mml:mo></mml:mover></mml:math> sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these âŠ
Abstract In this article, we introduce generalized beta extension of Sz $$\acute{a}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>a</mml:mi><mml:mo>ÂŽ</mml:mo></mml:mover></mml:math> sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin-type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections.. Moreover, numerical estimates and graphical representations for convergence of one- and two-dimensional sequences of operators are studied. In continuation, local and global approximation properties are studied in terms of the first- and second-order modulus of smoothness, Peetreâs K-functional and weight functions in various functional spaces.
<p style='text-indent:20px;'>The motive of this research article is to introduce a sequence of Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a}sz $\end{document}</tex-math></inline-formula> Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation âŠ
<p style='text-indent:20px;'>The motive of this research article is to introduce a sequence of Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a}sz $\end{document}</tex-math></inline-formula> Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in B<inline-formula><tex-math id="M3">\begin{document}$ \ddot{o} $\end{document}</tex-math></inline-formula>gel space via mixed modulus of continuity.
In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity âŠ
In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity in terms of well known Peetre?s K-functional, weighted approximation results, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in B?gel-spaces by use of mixed-modulus of continuity.
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f âŠ
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.
The objective of this paper is to construct univariate and bivariate blending type <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>α</a:mi></a:math> -SchurerâKantorovich operators depending on two parameters <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>α</c:mi><c:mo>â</c:mo><c:mfenced open="[" close="]" separators="|"><c:mrow><c:mn>0,1</c:mn></c:mrow></c:mfenced></c:math> and <h:math âŠ
The objective of this paper is to construct univariate and bivariate blending type <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>α</a:mi></a:math> -SchurerâKantorovich operators depending on two parameters <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>α</c:mi><c:mo>â</c:mo><c:mfenced open="[" close="]" separators="|"><c:mrow><c:mn>0,1</c:mn></c:mrow></c:mfenced></c:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M3"><h:mi>Ï</h:mi><h:mo>></h:mo><h:mn>0</h:mn></h:math> to approximate a class of measurable functions on <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" id="M4"><j:mfenced open="[" close="]" separators="|"><j:mrow><j:mn>0,1</j:mn><j:mo>+</j:mo><j:mi>q</j:mi></j:mrow></j:mfenced><j:mo>,</j:mo><j:mi>q</j:mi><j:mo>></j:mo><j:mn>0</j:mn></j:math> . We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetreâs <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M5"><o:mi>K</o:mi></o:math> -functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.
The aim of present article is to introduce the SzĂĄsz-Beta operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in âŠ
The aim of present article is to introduce the SzĂĄsz-Beta operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre's K-functional, second order modulus of smoothness, Lipschitz type space and rth order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results âŠ
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second order modulus of continuity, Peetres K-functional Lipschitz class.
In the present article, we introduced a new form of SzĂĄsz-type operators which preserves test functions e0 and e2(ei(t)=ti,i=0,2). By these sequence of positive linear operators, we gave rate of âŠ
In the present article, we introduced a new form of SzĂĄsz-type operators which preserves test functions e0 and e2(ei(t)=ti,i=0,2). By these sequence of positive linear operators, we gave rate of convergence and better error estimation by means of modulus of continuity. Moreover, we have discussed order of approximation with the help of local results. In the last, weighted Korovkin theorem is established.
We construct a novel family of summationâintegralâtype hybrid operators in terms of shape parameter α â [0,1] in this paper. Basic estimates, rate of convergence, and order of approximation are âŠ
We construct a novel family of summationâintegralâtype hybrid operators in terms of shape parameter α â [0,1] in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetreâs Kâfunctional, Lipschitz class, and secondâorder modulus of smoothness. The approximation results are then obtained in weighted space. Finally, for these operators q âstatistical convergence is also investigated.
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates, Korovkin-type theorems and direct approximation âŠ
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates, Korovkin-type theorems and direct approximation results using second order modulus of continuity, Peetreâs K-functional and Lipschitz class.
Abstract In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified SzĂĄszâDurrmeyer operators. We study the moments and basic results. Further, we âŠ
Abstract In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified SzĂĄszâDurrmeyer operators. We study the moments and basic results. Further, we investigate the pointwise approximation and uniform approximation results in various functional spaces for these sequences of positive linear operators. Finally, we prove the global approximation and A-statistical convergence results for these operators.
We construct a new version of q-Jakimovski-Leviatan type integral operators and show that set of all continuous functions f defined on [0,?) are uniformly approximated by our new operators. Finally âŠ
We construct a new version of q-Jakimovski-Leviatan type integral operators and show that set of all continuous functions f defined on [0,?) are uniformly approximated by our new operators. Finally we construct the Stancu type operators and obtain approximation properties in weighted spaces. Moreover, with the aid of modulus of continuity we discuss the rate of convergence, Lipschitz type maximal approximation and some direct theorems.
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators. Modulus of continuity, second modulus of âŠ
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators. Modulus of continuity, second modulus of continuity, Peeters K-functional, weighted modulus of continuity and Lipschitz class are considered to prove our results.
For a function $u(x)$ subharmonic (or ${C^2}$) in ${{\mathbf {R}}^m}$, we compare the ĂąÂÂharmonicsù (defined in ç1) of u with those of a related subharmonic function whose total Riesz mass âŠ
For a function $u(x)$ subharmonic (or ${C^2}$) in ${{\mathbf {R}}^m}$, we compare the ĂąÂÂharmonicsù (defined in ç1) of u with those of a related subharmonic function whose total Riesz mass in $|x| \leqslant r$ is the same as that of u, but whose ${L^2}$ norm on $|x| = r$ is maximal, for all $0 < r < \infty$. We deduce estimates on the growth of the Riesz mass of u in $|x| \leqslant r$, as $r \to \infty$.
In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to âŠ
In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetreâs K-functional and weight functions for these sequences in dierent spaces of functions.
The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. âŠ
The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.
This research work introduces a connection of adjoint Bernoulliâs polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators âŠ
This research work introduces a connection of adjoint Bernoulliâs polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional spaces with the aid of the Korovkin theorem, Voronovskaja-type theorem, first order of modulus of continuity, second order of modulus of continuity, Peetreâs K-functional, Lipschitz condition, etc. In the last section, we extend our research to a bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces. Moreover, we construct a numerical example to demonstrate the applicability of our results.
This research work focuses on λ-SzĂĄszâMirakjan operators coupling generalized beta function. The kernel functions used in λ-SzĂĄsz operators often possess even or odd symmetry. This symmetry influences the behavior of âŠ
This research work focuses on λ-SzĂĄszâMirakjan operators coupling generalized beta function. The kernel functions used in λ-SzĂĄsz operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approximation and convergence properties. The convergence properties, such as uniform convergence and pointwise convergence, are studied in view of the Korovkin theorem, the modulus of continuity, and Peetreâs K-functional of these sequences of positive linear operators in depth. Further, we extend our research work for the bivariate case of these sequences of operators. Their uniform rate of approximation and order of approximation are investigated in Lebesgue measurable spaces of function. The graphical representation and numerical error analysis in terms of the convergence behavior of these operators are studied.
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f âŠ
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.
The aim of this article is to introduce the Kantorovich form of generalized Szasz-type operators involving Charlier polynomials with certain parameters. In this paper we discussed the rate of convergence âŠ
The aim of this article is to introduce the Kantorovich form of generalized Szasz-type operators involving Charlier polynomials with certain parameters. In this paper we discussed the rate of convergence better error estimates and Korovkin-type theorem in polynomial weighted space. Further, we investigate the local approximation results with the help of Ditzian-Totik modulus of smoothness second order modulus of continuity Peetre's K functional and Lipschitz class.
In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for SzĂĄsz type operators using Sheffer polynomials.Lastly, we investigate statistical approximation for these âŠ
In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for SzĂĄsz type operators using Sheffer polynomials.Lastly, we investigate statistical approximation for these sequences.
In the present research article, we construct a new sequence of Generalized Bivariate Baskakov Durrmeyer Operators. We investigate rate of convergence and the order of approximation with the aid of âŠ
In the present research article, we construct a new sequence of Generalized Bivariate Baskakov Durrmeyer Operators. We investigate rate of convergence and the order of approximation with the aid of modulus of continuity in terms of well known Peetre?s K-functional, Voronovskaja type theorems and Lipschitz maximal functions. Further, graphical analysis is discussed. Moreover, we study the approximation properties of the operators in B?gel-spaces with the aid of mixed-modulus of continuity.
The aim of this article is to introduce a bivariate extension of Shurer-Stancu operators based on (p q)integers. We prove uniform approximation by means of Bohman Korovkin type theorem rate âŠ
The aim of this article is to introduce a bivariate extension of Shurer-Stancu operators based on (p q)integers. We prove uniform approximation by means of Bohman Korovkin type theorem rate of convergence using total modulus of smoothness and degree of approximation by using second order modulus of smoothness Peetres K functional Lipschitz type class.
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results âŠ
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second order modulus of continuity, Peetres K-functional Lipschitz class.
The aim of this article is to introduce a Stancu type generalization of modified Szasz operators using Charlier polynomials. We establish a recursive relation between Szasz-type operators defined in [S. âŠ
The aim of this article is to introduce a Stancu type generalization of modified Szasz operators using Charlier polynomials. We establish a recursive relation between Szasz-type operators defined in [S. Varma, F. Tasdelen, Szasz type operators involving Charlier polynomials, Math. Comput. Modeling 56 (5--6) (2012) 118--122] and Stancu-type generalization of these operators. Further, we discuss Korovkin type theorem, rate of convergence in terms of modulus of continuity and simultaneous approximation. Moreover, we study Local approximation results using second order modulus of smoothness, Peetre's K-functional and Lipschitz class. In the last of this manuscript, we give weighted Korovkin type theorem and statistical approximation result in polynomial weighted space.
In the present manuscript, we present a new sequence of operators, $i.e.$, $\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters $\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate measurable functions âŠ
In the present manuscript, we present a new sequence of operators, $i.e.$, $\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters $\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate measurable functions on $[0: 1+q], q>0$. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections. Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of first and second order modulus of smoothness, Peetre's K-functional and weight functions for these sequences in different spaces of functions.
We introduce the sequence of Stancu variant of ?-Schurer-Kantorovich operators and systematically investigate some basic estimates. We also obtain the uniform convergence theorem and the order of approximation in terms âŠ
We introduce the sequence of Stancu variant of ?-Schurer-Kantorovich operators and systematically investigate some basic estimates. We also obtain the uniform convergence theorem and the order of approximation in terms of suitable modulus of continuity for our newly defined operators. Moreover, we investigate rate of convergence by means of Peetre?s K-functional and local direct estimate via Lipschitz-type functions. Finally, A-statistical approximation is presented.
In the present research article, we construct a new family of summation-integral type hybrid operators in terms of shape parameter ? ? [0, 1]. Further, basic estimates, rate of convergence âŠ
In the present research article, we construct a new family of summation-integral type hybrid operators in terms of shape parameter ? ? [0, 1]. Further, basic estimates, rate of convergence and the order of approximation with the aid of Korovkin theorem and modulus of smoothness are investigated. Moreover, numerical simulation and graphical approximations are studied. For these sequences of positive linear operators, we study the local approximation results using Peetre?s K-functional, Lipschitz class and modulus of smoothness of second order. Next, we obtain the approximation results in weighted space. Lastly, A-statistical-approximation results are presented.
This manuscript associates with a study of FrobeniusâEulerâSimsek-type Polynomials. In this research work, we construct a new sequence of SzĂĄszâBeta type operators via FrobeniusâEulerâSimsek-type Polynomials to discuss approximation properties for âŠ
This manuscript associates with a study of FrobeniusâEulerâSimsek-type Polynomials. In this research work, we construct a new sequence of SzĂĄszâBeta type operators via FrobeniusâEulerâSimsek-type Polynomials to discuss approximation properties for the Lebesgue integrable functions, i.e., Lp[0,â), 1â€p<â. Furthermore, estimates in view of test functions and central moments are studied. Next, rate of convergence is discussed with the aid of the Korovkin theorem and the Voronovskaja type theorem. Moreover, direct approximation results in terms of modulus of continuity of first- and second-order, Peetreâs K-functional, Lipschitz type space, and the rth-order Lipschitz type maximal functions are investigated. In the subsequent section, we present weighted approximation results, and statistical approximation theorems are discussed. To demonstrate the effectiveness and applicability of the proposed operators, we present several illustrative examples and visualize the results graphically.
This study focuses on approximating continuous functions using FrobeniusâEulerâSimsek polynomial analogues of SzĂĄsz operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. âŠ
This study focuses on approximating continuous functions using FrobeniusâEulerâSimsek polynomial analogues of SzĂĄsz operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. Next, we investigate approximation order uniform convergence via Korovkin result and the modulus of smoothness for functions in continuous functional spaces. A Voronovskaja theorem is also explored approximating functions which belongs to the class of function having first and second order continuous derivative. Further, we discuss numerical error and graphical analysis. In the last, two dimensional operators are constructed to discuss approximation for the class of two variable continuous functions.
This research focuses on the approximation properties of Kantorovich-type operators using FrobeniusâEulerâSimsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and âŠ
This research focuses on the approximation properties of Kantorovich-type operators using FrobeniusâEulerâSimsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and the rate of approximation are analyzed using the classical Korovkin theorem and the modulus of continuity for Lebesgue measurable and continuous functions. A Voronovskaja-type theorem is also established to approximate functions with first- and second-order continuous derivatives. Numerical and graphical analyses are presented to support these findings. Furthermore, a bivariate sequence of these operators is introduced to approximate a bivariate class of Lebesgue measurable and continuous functions in two variables. Finally, numerical and graphical representations of the error are provided to check the rapidity of convergence.
The aim of present article is to introduce the SzĂĄsz-Beta-Schurer operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in âŠ
The aim of present article is to introduce the SzĂĄsz-Beta-Schurer operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetreâs K-functional, second order modulus of smoothness, Lipschitz type space and rth order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.
This research work focuses on λ-SzĂĄszâMirakjan operators coupling generalized beta function. The kernel functions used in λ-SzĂĄsz operators often possess even or odd symmetry. This symmetry influences the behavior of âŠ
This research work focuses on λ-SzĂĄszâMirakjan operators coupling generalized beta function. The kernel functions used in λ-SzĂĄsz operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approximation and convergence properties. The convergence properties, such as uniform convergence and pointwise convergence, are studied in view of the Korovkin theorem, the modulus of continuity, and Peetreâs K-functional of these sequences of positive linear operators in depth. Further, we extend our research work for the bivariate case of these sequences of operators. Their uniform rate of approximation and order of approximation are investigated in Lebesgue measurable spaces of function. The graphical representation and numerical error analysis in terms of the convergence behavior of these operators are studied.
This research work introduces a connection of adjoint Bernoulliâs polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators âŠ
This research work introduces a connection of adjoint Bernoulliâs polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional spaces with the aid of the Korovkin theorem, Voronovskaja-type theorem, first order of modulus of continuity, second order of modulus of continuity, Peetreâs K-functional, Lipschitz condition, etc. In the last section, we extend our research to a bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces. Moreover, we construct a numerical example to demonstrate the applicability of our results.
The goal of this manuscript is to introduce a new sequence of generalized-Baskakov Durrmeyer-Schurer Operators. Further, basic estimates are calculated. In the subsection sequence, rapidity of convergence and order of âŠ
The goal of this manuscript is to introduce a new sequence of generalized-Baskakov Durrmeyer-Schurer Operators. Further, basic estimates are calculated. In the subsection sequence, rapidity of convergence and order of approximation are studied in terms of first and second-order modulus of continuity. We prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Moreover, local and global approximation properties are discussed in different functional spaces. Lastly, A-statistical approximation results are presented.
The aim of present article is to introduce the SzĂĄsz-Beta operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in âŠ
The aim of present article is to introduce the SzĂĄsz-Beta operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre's K-functional, second order modulus of smoothness, Lipschitz type space and rth order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.
In the present work, we introduce paranormed zweier ideal convergent triple sequence spaces defined by a compact operator 3ZI(?), 3ZI0 (?) and 3ZI? (?) where q = (qijk) is a âŠ
In the present work, we introduce paranormed zweier ideal convergent triple sequence spaces defined by a compact operator 3ZI(?), 3ZI0 (?) and 3ZI? (?) where q = (qijk) is a triple sequence of positive numbers and we study some algebraic and topological properties of these spaces.
The concept of fuzzy sets was introduced by Zadeh as a means of representing data that was not precise but rather fuzzy. Recently, Kocinac [19] studied some topological properties of âŠ
The concept of fuzzy sets was introduced by Zadeh as a means of representing data that was not precise but rather fuzzy. Recently, Kocinac [19] studied some topological properties of fuzzy antinormed linear spaces. This has motivated us to introduce and study the fuzzy antinormed double sequence spaces with respect to ideal by using a bounded linear operator and prove some theorems, in particular convergence and completeness theorems on these new double sequence spaces.
The objective of this paper is to construct univariate and bivariate blending type <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>α</a:mi></a:math> -SchurerâKantorovich operators depending on two parameters <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>α</c:mi><c:mo>â</c:mo><c:mfenced open="[" close="]" separators="|"><c:mrow><c:mn>0,1</c:mn></c:mrow></c:mfenced></c:math> and <h:math âŠ
The objective of this paper is to construct univariate and bivariate blending type <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>α</a:mi></a:math> -SchurerâKantorovich operators depending on two parameters <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>α</c:mi><c:mo>â</c:mo><c:mfenced open="[" close="]" separators="|"><c:mrow><c:mn>0,1</c:mn></c:mrow></c:mfenced></c:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M3"><h:mi>Ï</h:mi><h:mo>></h:mo><h:mn>0</h:mn></h:math> to approximate a class of measurable functions on <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" id="M4"><j:mfenced open="[" close="]" separators="|"><j:mrow><j:mn>0,1</j:mn><j:mo>+</j:mo><j:mi>q</j:mi></j:mrow></j:mfenced><j:mo>,</j:mo><j:mi>q</j:mi><j:mo>></j:mo><j:mn>0</j:mn></j:math> . We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetreâs <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M5"><o:mi>K</o:mi></o:math> -functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.
Abstract In this article, we introduce generalized beta extension of Sz $$\acute{a}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>a</mml:mi><mml:mo>ÂŽ</mml:mo></mml:mover></mml:math> sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these âŠ
Abstract In this article, we introduce generalized beta extension of Sz $$\acute{a}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>a</mml:mi><mml:mo>ÂŽ</mml:mo></mml:mover></mml:math> sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin-type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections.. Moreover, numerical estimates and graphical representations for convergence of one- and two-dimensional sequences of operators are studied. In continuation, local and global approximation properties are studied in terms of the first- and second-order modulus of smoothness, Peetreâs K-functional and weight functions in various functional spaces.
In the present research article, we construct a new family of summation-integral type hybrid operators in terms of shape parameter ? ? [0, 1]. Further, basic estimates, rate of convergence âŠ
In the present research article, we construct a new family of summation-integral type hybrid operators in terms of shape parameter ? ? [0, 1]. Further, basic estimates, rate of convergence and the order of approximation with the aid of Korovkin theorem and modulus of smoothness are investigated. Moreover, numerical simulation and graphical approximations are studied. For these sequences of positive linear operators, we study the local approximation results using Peetre?s K-functional, Lipschitz class and modulus of smoothness of second order. Next, we obtain the approximation results in weighted space. Lastly, A-statistical-approximation results are presented.
We construct a new version of q-Jakimovski-Leviatan type integral operators and show that set of all continuous functions f defined on [0,?) are uniformly approximated by our new operators. Finally âŠ
We construct a new version of q-Jakimovski-Leviatan type integral operators and show that set of all continuous functions f defined on [0,?) are uniformly approximated by our new operators. Finally we construct the Stancu type operators and obtain approximation properties in weighted spaces. Moreover, with the aid of modulus of continuity we discuss the rate of convergence, Lipschitz type maximal approximation and some direct theorems.
<p style='text-indent:20px;'>The motive of this research article is to introduce a sequence of Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a}sz $\end{document}</tex-math></inline-formula> Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation âŠ
<p style='text-indent:20px;'>The motive of this research article is to introduce a sequence of Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a}sz $\end{document}</tex-math></inline-formula> Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in B<inline-formula><tex-math id="M3">\begin{document}$ \ddot{o} $\end{document}</tex-math></inline-formula>gel space via mixed modulus of continuity.
The goal of this research article is to introduce a sequence of αâStancuâSchurerâKantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of âŠ
The goal of this research article is to introduce a sequence of αâStancuâSchurerâKantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional αâStancuâSchurerâKantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented.
We construct a novel family of summationâintegralâtype hybrid operators in terms of shape parameter α â [0,1] in this paper. Basic estimates, rate of convergence, and order of approximation are âŠ
We construct a novel family of summationâintegralâtype hybrid operators in terms of shape parameter α â [0,1] in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetreâs Kâfunctional, Lipschitz class, and secondâorder modulus of smoothness. The approximation results are then obtained in weighted space. Finally, for these operators q âstatistical convergence is also investigated.
<p style='text-indent:20px;'>The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a} $\end{document}</tex-math></inline-formula>sz-Schurer-Beta type operators to approximate a class of Lebesgue âŠ
<p style='text-indent:20px;'>The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a} $\end{document}</tex-math></inline-formula>sz-Schurer-Beta type operators to approximate a class of Lebesgue integrable functions. Moreover, we calculate basic estimates and central moments for these sequences of operators. Further, rapidity of convergence and order of approximation are investigated in terms of Korovkin theorem and modulus of smoothess. In subsequent section, local and global approximation properties are studied in various functional spaces.</p>
In the present research article, we construct a new sequence of Generalized Bivariate Baskakov Durrmeyer Operators. We investigate rate of convergence and the order of approximation with the aid of âŠ
In the present research article, we construct a new sequence of Generalized Bivariate Baskakov Durrmeyer Operators. We investigate rate of convergence and the order of approximation with the aid of modulus of continuity in terms of well known Peetre?s K-functional, Voronovskaja type theorems and Lipschitz maximal functions. Further, graphical analysis is discussed. Moreover, we study the approximation properties of the operators in B?gel-spaces with the aid of mixed-modulus of continuity.
In the present manuscript, we present a new sequence of operators, $i.e.$, $\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters $\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate measurable functions âŠ
In the present manuscript, we present a new sequence of operators, $i.e.$, $\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters $\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate measurable functions on $[0: 1+q], q>0$. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections. Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of first and second order modulus of smoothness, Peetre's K-functional and weight functions for these sequences in different spaces of functions.
We introduce the sequence of Stancu variant of ?-Schurer-Kantorovich operators and systematically investigate some basic estimates. We also obtain the uniform convergence theorem and the order of approximation in terms âŠ
We introduce the sequence of Stancu variant of ?-Schurer-Kantorovich operators and systematically investigate some basic estimates. We also obtain the uniform convergence theorem and the order of approximation in terms of suitable modulus of continuity for our newly defined operators. Moreover, we investigate rate of convergence by means of Peetre?s K-functional and local direct estimate via Lipschitz-type functions. Finally, A-statistical approximation is presented.
In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to âŠ
In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetreâs K-functional and weight functions for these sequences in dierent spaces of functions.
The main purpose of this article is to study the bivariate approximation generalization for Baskakov-Durrmeyer-operators with the aid of non-negative parametric variants suppose 0 ? ?1,?2 ? 1. We obtain âŠ
The main purpose of this article is to study the bivariate approximation generalization for Baskakov-Durrmeyer-operators with the aid of non-negative parametric variants suppose 0 ? ?1,?2 ? 1. We obtain the order of approximation by use of the modulus of continuity in terms of well known Peetre?s K-functional, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in B?gel-spaces by use of mixed-modulus of continuity.
In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity âŠ
In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity in terms of well known Peetre?s K-functional, weighted approximation results, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in B?gel-spaces by use of mixed-modulus of continuity.
Abstract In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified SzĂĄszâDurrmeyer operators. We study the moments and basic results. Further, we âŠ
Abstract In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified SzĂĄszâDurrmeyer operators. We study the moments and basic results. Further, we investigate the pointwise approximation and uniform approximation results in various functional spaces for these sequences of positive linear operators. Finally, we prove the global approximation and A-statistical convergence results for these operators.
In the present manuscript, we define a non-negative parametric variant of BaskakovâDurrmeyer operators to study the convergence of Lebesgue measurable functions and introduce these as α-BaskakovâDurrmeyer operators. We study the âŠ
In the present manuscript, we define a non-negative parametric variant of BaskakovâDurrmeyer operators to study the convergence of Lebesgue measurable functions and introduce these as α-BaskakovâDurrmeyer operators. We study the uniform convergence of these operators in weighted spaces.
The aim of this article is to introduce a Stancu type generalization of modified Szasz operators using Charlier polynomials. We establish a recursive relation between Szasz-type operators defined in [S. âŠ
The aim of this article is to introduce a Stancu type generalization of modified Szasz operators using Charlier polynomials. We establish a recursive relation between Szasz-type operators defined in [S. Varma, F. Tasdelen, Szasz type operators involving Charlier polynomials, Math. Comput. Modeling 56 (5--6) (2012) 118--122] and Stancu-type generalization of these operators. Further, we discuss Korovkin type theorem, rate of convergence in terms of modulus of continuity and simultaneous approximation. Moreover, we study Local approximation results using second order modulus of smoothness, Peetre's K-functional and Lipschitz class. In the last of this manuscript, we give weighted Korovkin type theorem and statistical approximation result in polynomial weighted space.
The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of SzĂĄsz type operators known as Phillips operators. To âŠ
The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of SzĂĄsz type operators known as Phillips operators. To achieve the results of a better way of uniform convergence of the Phillips operators, we study qualitative results in a Korovkin and weighted Korovkin space.
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates, Korovkin-type theorems and direct approximation âŠ
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates, Korovkin-type theorems and direct approximation results using second order modulus of continuity, Peetreâs K-functional and Lipschitz class.
In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. âŠ
In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. In the last, we prove weighted approximation results.
The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence âŠ
The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre?s K-functional, Lipschitz type class.
The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. âŠ
The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.
In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for SzĂĄsz type operators using Sheffer polynomials.Lastly, we investigate statistical approximation for these âŠ
In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for SzĂĄsz type operators using Sheffer polynomials.Lastly, we investigate statistical approximation for these sequences.
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f âŠ
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.
In the present article, we introduced a new form of SzĂĄsz-type operators which preserves test functions e0 and e2(ei(t)=ti,i=0,2). By these sequence of positive linear operators, we gave rate of âŠ
In the present article, we introduced a new form of SzĂĄsz-type operators which preserves test functions e0 and e2(ei(t)=ti,i=0,2). By these sequence of positive linear operators, we gave rate of convergence and better error estimation by means of modulus of continuity. Moreover, we have discussed order of approximation with the help of local results. In the last, weighted Korovkin theorem is established.
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators.Modulus of continuity, second modulus of continuity, âŠ
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators.Modulus of continuity, second modulus of continuity, Peeter's K-functional, weighted modulus of continuity and Lipschitz class are considered to prove our results.
In the present paper, we construct a new sequence of BernsteinâKantorovich operators depending on a parameter α . The uniform convergence of the operators and rate of convergence in local âŠ
In the present paper, we construct a new sequence of BernsteinâKantorovich operators depending on a parameter α . The uniform convergence of the operators and rate of convergence in local and global sense in terms of firstâ and secondâorder modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of BernsteinâKantorovich operators and their approximation behaviors.
In this paper, we consider a certain King type operators which includes general families of SzĂĄsz-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, âŠ
In this paper, we consider a certain King type operators which includes general families of SzĂĄsz-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, which provides global approximation for the above mentioned operators, we obtain the rate of convergence of this class. Furthermore, we give local approximation results by using the first and the second modulus of continuity.
The paper studi es t he convergence of P (u, x) to f (x) as u -> 00 .The resul ts obtained are generalized anal ogs, for the interval 0 âŠ
The paper studi es t he convergence of P (u, x) to f (x) as u -> 00 .The resul ts obtained are generalized anal ogs, for the interval 0 :
In this paper we prove some Korovkin and Weierstrass type approximation theorems via statistical convergence.We are also concerned with the order of statistical convergence of a sequence of positive linear âŠ
In this paper we prove some Korovkin and Weierstrass type approximation theorems via statistical convergence.We are also concerned with the order of statistical convergence of a sequence of positive linear operators.
This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the âŠ
This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator calculus, which generalizes the calculus associated with the quantum mechanical simple harmonic oscillator, is studied in terms of these polynomials.
In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly CesĂ ro and statistically C1q-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, âŠ
In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly CesĂ ro and statistically C1q-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly CesĂ ro and statistically C1q-summable sequences. Further, we apply q-statistical convergence to prove a Korovkin type approximation theorem.
In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence âŠ
In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [Formula: see text] to [Formula: see text], and we see that in some cases the errors are smaller than [Formula: see text] to f.
We construct the linear positive operators generated by the q-Dunkl generalization of the exponential function. We have approximation properties of the operators via a universal Korovkin-type theorem and a weighted âŠ
We construct the linear positive operators generated by the q-Dunkl generalization of the exponential function. We have approximation properties of the operators via a universal Korovkin-type theorem and a weighted Korovkin-type theorem. The rate of convergence of the operators for functions belonging to the Lipschitz class is presented. We obtain the rate of convergence by means of the classical, second order, and weighted modulus of continuity, respectively, as well.
Using $A$-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function $f$ by means of a sequence $\{T_{n}(f;x)\}$ of positive linear operators acting âŠ
Using $A$-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function $f$ by means of a sequence $\{T_{n}(f;x)\}$ of positive linear operators acting from a weighted space $C_{\varrho_{1}}
The present paper deals with genuine Bernstein-Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre [Formula: see text]-functional and corresponding modulus of âŠ
The present paper deals with genuine Bernstein-Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre [Formula: see text]-functional and corresponding modulus of smoothness, quantitative Voronovskaya type theorem and GrĂŒss-Voronovskaya type theorem in quantitative mean are discussed. Finally, the graphic for new operators with special cases and for some values of n is also presented.
The object of this paper to construct Dunkl type SzĂĄsz operators via post-quantum calculus. We obtain some approximation results for these new operators and compute convergence of the operators by âŠ
The object of this paper to construct Dunkl type SzĂĄsz operators via post-quantum calculus. We obtain some approximation results for these new operators and compute convergence of the operators by using the modulus of continuity. Furthermore, we obtain the rate of convergence of these operators for functions belonging to the Lipschitz class. We also study the bivariate version of these operators.
In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity âŠ
In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate the order of approximation with the aid of modulus of continuity in terms of well known Peetre?s K-functional, weighted approximation results, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in B?gel-spaces by use of mixed-modulus of continuity.
The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of SzĂĄsz type operators known as Phillips operators. To âŠ
The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of SzĂĄsz type operators known as Phillips operators. To achieve the results of a better way of uniform convergence of the Phillips operators, we study qualitative results in a Korovkin and weighted Korovkin space.
In the present work, we construct a new sequence of positive linear operatorsinvolving PĂłlya distribution. We compute a Voronovskaja type and a GrĂŒssâVoronovskaja type asymptotic formula as well as the âŠ
In the present work, we construct a new sequence of positive linear operatorsinvolving PĂłlya distribution. We compute a Voronovskaja type and a GrĂŒssâVoronovskaja type asymptotic formula as well as the rate of approximation by using the modulus of smoothness and for functions in a Lipschitz type space. Lastly, we provide some numerical results, which explain the validity of the theoretical results and the effectiveness of the constructed operators.
Abstract We construct the bivariate form of BernsteinâSchurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the âŠ
Abstract We construct the bivariate form of BernsteinâSchurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetreâs K -functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
In this work, we investigate some approximation properties of blending type univariate and bivariate Schurer-Kantorovich operators based on shape parameter λ â [â1, 1]. We evaluate some moment estimates and âŠ
In this work, we investigate some approximation properties of blending type univariate and bivariate Schurer-Kantorovich operators based on shape parameter λ â [â1, 1]. We evaluate some moment estimates and obtain several direct theorems. Next, we construct the bivariate version of proposed operators and compute rate of approximation with the partial and complete modulus of continuity. Moreover, we present certain graphical and numerical results for univariate and bivariate versions of these operators.
In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λâ[â1,1]λâ[â1,1]. Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate âŠ
In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λâ[â1,1]λâ[â1,1]. Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.
Our aim is to define modified Sz?sz type operators involving Charlier polynomials and obtain some approximation properties. We prove some results on the order of convergence by using the modulus âŠ
Our aim is to define modified Sz?sz type operators involving Charlier polynomials and obtain some approximation properties. We prove some results on the order of convergence by using the modulus of smoothness and Peetre?s K-functional. We also establish Voronoskaja type theorem for these operators. Moreover, we prove a Korovkin type approximation theorem via q-statistical convergence.
An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, âŠ
An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of BernsteinâKantorovich operators involving shape parameters λ, α and a positive integer as an original extension of BernsteinâKantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.
Herein we propose a non-negative real parametric generalization of the Baskakov operators and call them as $\alpha$-Baskakov operators. We show that $\alpha$-Baskakov operators can be expressed in terms of divided âŠ
Herein we propose a non-negative real parametric generalization of the Baskakov operators and call them as $\alpha$-Baskakov operators. We show that $\alpha$-Baskakov operators can be expressed in terms of divided differences. Then, we obtain $n$th order derivative of $\alpha$-Baskakov operators in order to obtain its new representation as powers of independent variable $x$. In addition, we obtain Korovkinâs type approximation properties of $\alpha$-Baskakov operators. Moreover, by using the modulus of continuity, we obtain the rate of convergence. Numerical results presented show that depending on the value of the parameter $\alpha$, an approximation to a function improves compared to the classical Baskakov operators.
The aim of the present paper is to introduce a Kantorovich-type modification ofthe q-discrete beta operators and to investigate their statistical andweighted statistical approximation properties. Rates of statistical convergenceby means âŠ
The aim of the present paper is to introduce a Kantorovich-type modification ofthe q-discrete beta operators and to investigate their statistical andweighted statistical approximation properties. Rates of statistical convergenceby means of the modulus of continuity and the Lipschitz-type function are alsoestablished for operators. Finally, we construct a bivariate generalization ofthe operator and also obtain the statistical approximation properties. MSC: 41A25, 41A36.
In the present paper, we introduce Bernstein-Chlodowsky-Gadjiev operators taking into consideration the polynomials introduced by Gadjiev and Ghorbanalizadeh [2]. The interval of convergence of the operators is a moved interval âŠ
In the present paper, we introduce Bernstein-Chlodowsky-Gadjiev operators taking into consideration the polynomials introduced by Gadjiev and Ghorbanalizadeh [2]. The interval of convergence of the operators is a moved interval as polynomials given in [2] but grows as n ( â as in the classical Bernstein-Chlodowsky polynomials. Also their knots are shifted and depend on x. We firstly study weighted approximation properties of these operators and show that these operators are more efficient in weighted approximating to function having polynomial growth since these operators contain a factor bn tending to infinity. Secondly we calculate derivative of new Bernstein-Chlodowsky-Gadjiev operators and give a weighted approximation theorem in Lipchitz space for the derivatives of these operators.
In the present paper, we introduce Stancu type generalization of (p,q)-Szasz-Mirakyan-Baskakov operators and investigate their approximation properties such as weighted approximation, rate of convergence and pointwise convergence.
In the present paper, we introduce Stancu type generalization of (p,q)-Szasz-Mirakyan-Baskakov operators and investigate their approximation properties such as weighted approximation, rate of convergence and pointwise convergence.
The present paper deals with the construction of Baskakov Durrmeyer operators, which preserve the linear functions, in (p,q) -calculus.More precisely, using (p,q) -Gamma function we introduce genuine mixed type Baskakov âŠ
The present paper deals with the construction of Baskakov Durrmeyer operators, which preserve the linear functions, in (p,q) -calculus.More precisely, using (p,q) -Gamma function we introduce genuine mixed type Baskakov Durrmeyer operators having Baskakov and SzĂĄsz basis functions.After construction of the operators and calculations of their moments and central moments, rate of convergence of the operators by means of appropriate modulus of continuity, approximation behaviors for functions belong to Lipschitz class and weighted approximation are explored.
The main purpose of the present article is to construct a newly SzĂĄsz-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate âŠ
The main purpose of the present article is to construct a newly SzĂĄsz-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>A</mml:mi></mml:math>-statistical convergence of operators and approximation properties of the bivariate case.
In the present article, we introduced a new form of SzĂĄsz-type operators which preserves test functions e0 and e2(ei(t)=ti,i=0,2). By these sequence of positive linear operators, we gave rate of âŠ
In the present article, we introduced a new form of SzĂĄsz-type operators which preserves test functions e0 and e2(ei(t)=ti,i=0,2). By these sequence of positive linear operators, we gave rate of convergence and better error estimation by means of modulus of continuity. Moreover, we have discussed order of approximation with the help of local results. In the last, weighted Korovkin theorem is established.