Arun Kajla

Generalized Baskakov-Szász type operators

Abstract In the present paper, we introduce generalized Baskakov-Szasz type operators and study some approximation properties of these operators e.g., rate of convergence in ordinary and simultaneous approximation, statistical convergence and the estimate of the rate of convergence for absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation.

Szász-Durrmeyer type operators based on Charlier polynomials

In the present paper, we introduce a Durrmeyer type modification of Szasz operators based on Charlier polynomials and study a Voronovskaja type asymptotic theorem, local approximation theorem, weighted approximation, statistical convergence and approximation of functions with derivatives of bounded variation for these operators.

q - Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables

The purpose of this paper is to obtain some direct results for the Durrmeyer variant of q - Bernstein-Schurer operators for functions of one variable introduced by Acu et?al. 1. We also propose to study the bivariate extension of these operators and discuss the rate of convergence by using the modulus of continuity, the degree of approximation for the Lipschitz class of functions and the Voronovskaja type asymptotic theorem. Furthermore, we show the convergence of the operators by illustrative graphics in Maple to certain functions in both one and two dimensional cases.

Approximation properties of Bezier-summation-integral type operators based on Polya-Bernstein functions

In this article we introduce the Bezier variant of summation integral type operators having Polya and Bernstein basis functions. We give a direct approximation theorem by means of the first order modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

Rate of convergence of Lupas Kantorovich operators based on Polya distribution

In the present paper, we consider the Kantorovich modification of Lupas operators based on Polya distribution. We estimate the rate of convergence for absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation.

The Kantorovich variant of an operator defined by D. D. Stancu

In this note we introduce Kantorovich variant of the operators considered by Stancu (1998) based on two nonnegative parameters. Here, we prove an approximation theorem with the help of Bohman–Korovkin’s principle and find the estimate of the rate of convergence by means of modulus of smoothness and Lipschitz type function for these operators. In the last section of the paper, we show the convergence of the operators by illustrative graphics in Mathematica to certain functions.

Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution

Abstract In the paper the authors introduce the Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, such as Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are bounded is also obtained.

Modified Baskakov-Szász Operators Based on q-Integers

In the present paper we introduce the Stancu variant of certain q-modified Baskakov \(Sz\acute{a}sz\) operators. We estimate the moments of the operators and obtain some direct results in terms of the modulus of continuity. Then, we study the Voronovskaja type theorem and the rate of convergence of these operators in terms of the weighted modulus of continuity. Further, we discuss the point-wise estimation using the Lipschitz type maximal function. Finally, we investigate the rate of statistical convergence of these operators using weighted modulus of continuity.