Meenu Goyal

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.

Quantitative convergence results for a family of hybrid operators

We introduce a one parameter family of hybrid operators and study quantitative convergence theorems for these operators e.g. local and weighted approximation results and simultaneous approximation of derivatives. Further, we discuss the statistical convergence of these operators. Lastly, we show the rate of convergence of these operators to a certain function by illustrative graphics in Matlab.

General Gamma type operators based on q-integers

In the present paper, we introduce the q-analogue of the general Gamma type operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Further, we study the A -statistical convergence of these operators. Lastly, we propose a king type modification of these operators to obtain better estimates.

Szász-Baskakov type operators based on q-integers

In the present paper, we introduce the q-analog of the Stancu variant of Szász-Baskakov operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Lastly, we study the A-statistical convergence of these operators and also, in order to obtain a better approximation, we study a King type modification of the above operators.MSC:41A25, 26A15, 40A35.

Bivariate Extension of Linear Positive Operators

The goal of this chapter is to present a survey of the literature on approximation of functions of two variables by linear positive operators. We study the approximation properties of these operators in the space of functions of two variables, continuous on a compact set. We also discuss the convergence of the operators in a weighted space of functions of two variables and find the rate of this convergence by means of modulus of continuity.

Degree of Approximation by Certain Genuine Hybrid Operators

This paper is in continuation of our work on certain genuine hybrid operators in (Positivity (Under review)) [3]. First, we discuss some direct results in simultaneous approximation by these operators, e.g. pointwise convergence theorem, Voronovskaja-type theorem and an error estimate in terms of the modulus of continuity. Next, we estimate the rate of convergence for functions having a derivative that coincides a.e. with a function of bounded variation.