Statistical weighted (Nλ,p,q)(Eλ,1)A-summability with application to Korovkin's type approximation theorem

In this paper, we first introduce the notion of statistical weighted (Nλ,p,q)(Eλ,1)A-summability and then investigate its relation with the weighted (Nλ,p,q)(Eλ,1)A-statistical convergence. We also study the weighted (Nλ,p,q)(Eλ,1)-regular matrix and find the conditions for the matrix A to be weight...

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Bibliographic Details
Published in:Bulletin des sciences mathématiques 2022-09, Vol.178, p.103146, Article 103146
Main Authors: Srivastava, H.M., Aljimi, Ekrem, Hazarika, Bipan
Format: Article
Language:English
Subjects:
A-statistical convergence
Korovkin type approximation theorems
Modulus of continuity
Nonnegative regular matrix
Statistical weighted summability
Test functions
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Summary:In this paper, we first introduce the notion of statistical weighted (Nλ,p,q)(Eλ,1)A-summability and then investigate its relation with the weighted (Nλ,p,q)(Eλ,1)A-statistical convergence. We also study the weighted (Nλ,p,q)(Eλ,1)-regular matrix and find the conditions for the matrix A to be weighted (Nλ,p,q)(Eλ,1)-regular. Furthermore, as an application of the results presented in this paper, we prove a Korovkin type approximation theorem involving the statistical weighted (Nλ,p,q)(Eλ,1)A-summability, which we have introduced in this paper. Relevant connections of the proposed investigation with other recent developments on the subject are also indicated.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2022.103146