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Journal of Applied Analysis

Editor-in-Chief: Fechner, Włodzimierz / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

CiteScore 2018: 0.45

SCImago Journal Rank (SJR) 2018: 0.181
Source Normalized Impact per Paper (SNIP) 2018: 0.845

Mathematical Citation Quotient (MCQ) 2018: 0.20

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1869-6082
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Volume 24, Issue 1

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

H. M. Srivastava
• Corresponding author
• Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada; and Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, P. R. China
• Email
• Other articles by this author:
/ Bidu Bhusan Jena
/ Susanta Kumar Paikray
/ U. K. Misra
• Department of Mathematics, National Institute of Science and Technology, Palur Hills, Golanthara 761008, Odisha, India
• Email
• Other articles by this author:
Published Online: 2018-05-03 | DOI: https://doi.org/10.1515/jaa-2018-0001

Abstract

Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and $\mathcal{𝒜}$-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 $\mathcal{𝒜}$-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and ${t}^{2}$ defined on a Banach space $C\left[0,1\right]$ for a sequence of (presumably new) positive linear operators based upon $\left(p,q\right)$-Lagrange polynomials. Furthermore, we investigate the deferred weighted $\mathcal{𝒜}$-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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Accepted: 2018-04-12

Published Online: 2018-05-03

Published in Print: 2018-06-01

Citation Information: Journal of Applied Analysis, Volume 24, Issue 1, Pages 1–16, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908,

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© 2018 Walter de Gruyter GmbH, Berlin/Boston.

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