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

Deferred weighted π’œ-statistical convergence based upon the (p,q)-Lagrange polynomials and its... AbstractRecently, the notion of positive linear operatorsby means of basic (or q-) Lagrangepolynomials and π’œ{\mathcal{A}}-statistical convergence was introducedand 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 deferredweighted π’œ{\mathcal{A}}-statistical convergence in order to establish someKorovkin-type approximation theorems associated with the functions1, t and t2{t^{2}}defined on a Banach space C⁒[0,1]{C[0,1]}for asequence of (presumably new) positive linear operators based upon(p,q){(p,q)}-Lagrange polynomials. Furthermore, we investigate thedeferred weighted π’œ{\mathcal{A}}-statistical rates for the same set offunctions with the help of the modulus of continuity and theelements of the Lipschitz class. We also consider a number ofinteresting special cases and illustrative examples in support ofour definitions and of the results whichare presented in this paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

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

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Publisher
De Gruyter
Copyright
Β© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
D.O.I.
10.1515/jaa-2018-0001
Publisher site
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Abstract

AbstractRecently, the notion of positive linear operatorsby means of basic (or q-) Lagrangepolynomials and π’œ{\mathcal{A}}-statistical convergence was introducedand 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 deferredweighted π’œ{\mathcal{A}}-statistical convergence in order to establish someKorovkin-type approximation theorems associated with the functions1, t and t2{t^{2}}defined on a Banach space C⁒[0,1]{C[0,1]}for asequence of (presumably new) positive linear operators based upon(p,q){(p,q)}-Lagrange polynomials. Furthermore, we investigate thedeferred weighted π’œ{\mathcal{A}}-statistical rates for the same set offunctions with the help of the modulus of continuity and theelements of the Lipschitz class. We also consider a number ofinteresting special cases and illustrative examples in support ofour definitions and of the results whichare presented in this paper.

Journal

Journal of Applied Analysisde Gruyter

Published: Jun 1, 2018

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