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

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

Journal of Applied Analysis, Volume 24 (1): 16 – Jun 1, 2018
16 pages

1

/lp/degruyter/deferred-weighted-statistical-convergence-based-upon-the-p-q-lagrange-zX5VH3Ody0
Publisher
de Gruyter
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
D.O.I.
10.1515/jaa-2018-0001
Publisher site
See Article on Publisher Site

### Abstract

AbstractRecently, the notion of positive linear operatorsby means of basic (or q-) Lagrangepolynomials and 𝒜{\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 𝒜{\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 𝒜{\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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations