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Journal of Applied Analysis

Editor-in-Chief: Fechner, WƂodzimierz / 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

Issues

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
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ 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:
  • De Gruyter OnlineGoogle Scholar
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 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.

Keywords: Statistical convergence; Korovkin-type approximation theorems; rate of convergence; modulus of continuity; Lipschitz class; Lagrange polynomials; Chan–Chyan–Srivastava polynomials

MSC 2010: 40A05; 41A36; 40G15

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About the article

Received: 2018-02-24

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, DOI: https://doi.org/10.1515/jaa-2018-0001.

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