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Kyungpook Mathematical Journal -0001; 56(3): 877-897

Published online November 30, -0001

Copyright © Kyungpook Mathematical Journal.

Szász-Kantorovich Type Operators Based on Charlier Polynomials

Arun Kajla, Purshottam Narain Agrawal

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India

Received: November 21, 2015; Accepted: April 7, 2016

Abstract

In the present article, we study some approximation properties of the Kantorovich type generalization of Szász type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5–6) (2012) 108–112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.

Keywords: Kantorovich operator, Charlier polynomials, modulus of continuity, $A$-statistical convergence, bounded variation.