Weighted statistical convergence based on generalized difference operator involving (p, q)-gamma function and its applications to approximation theorems


Kadak U.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.448, no.2, pp.1633-1650, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 448 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1016/j.jmaa.2016.11.084
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1633-1650
  • Keywords: The difference operator Delta(alpha,beta,gamma)(h,p,q), Weighted statistical convergence and statistical summability, (p, q)-analogue of Bernstein-Schurer operator, Korovkin type approximations for functions of two variables, The rate of convergence, SEQUENCE-SPACES, FRACTIONAL ORDER, KOROVKIN
  • Gazi University Affiliated: Yes

Abstract

In this work, following a new approach of Baliarsingh (2016) [6], we introduce the concepts of statistically weighted Psi(p,q)(Delta)-summability, weighted Psi(p,q)(Delta)-statistical convergence and weighted strongly Psi(p,q)(Delta)-summability with respect to the difference operatorh Delta(alpha,beta,gamma)(h,p,q) including (p, q)-analogue of Gamma function. Some inclusion,, relations between newly proposed methods are examined. We then prove a Korovkin type approximation theorem for functions of two variables and also present an example via (p, q)-analogue of modified Bernstein-Schurer operators to show that our proposed method is stronger than its classical and weighted statistical versions. Furthermore, we compute the rate of convergence of approximating positive linear operators through the modulus of continuity. Finally, we present computational and geometrical approaches to illustrate some of our results in this paper. (C) 2016 Elsevier Inc. All rights reserved.