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Deferred weighted 𝒜-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems

  • H. M. Srivastava EMAIL logo , Bidu Bhusan Jena , Susanta Kumar Paikray and U. K. Misra
Published/Copyright: May 3, 2018

Abstract

Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and 𝒜-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911–6918]. In our present investigation, we introduce a certain deferred weighted 𝒜-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and t2 defined on a Banach space Cⁱ[0,1] for a sequence of (presumably new) positive linear operators based upon (p,q)-Lagrange polynomials. Furthermore, we investigate the deferred weighted 𝒜-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

MSC 2010: 40A05; 41A36; 40G15

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Received: 2018-2-24
Accepted: 2018-4-12
Published Online: 2018-5-3
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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