Statistical weighted A-summability with application to Korovkin’s type approximation theorem

Abstract We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be weighted regular. As an application, w...

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Main Author:	Syed Abdul Mohiuddine
Format:	Article
Language:	English
Published:	SpringerOpen 2016-03-01
Series:	Journal of Inequalities and Applications
Subjects:	statistical convergence statistical weighted A-summability regular matrix positive linear operator Korovkin theorem
Online Access:	http://link.springer.com/article/10.1186/s13660-016-1040-1

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spelling	doaj-019d39523b9045a083942155ed1ec59d2020-11-24T21:50:40ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-03-012016111310.1186/s13660-016-1040-1Statistical weighted A-summability with application to Korovkin’s type approximation theoremSyed Abdul Mohiuddine0Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz UniversityAbstract We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be weighted regular. As an application, we prove the Korovkin type approximation theorem through statistical weighted A-summability and using the BBH operator to construct an illustrative example in support of our result.http://link.springer.com/article/10.1186/s13660-016-1040-1statistical convergencestatistical weighted A-summabilityregular matrixpositive linear operatorKorovkin theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Syed Abdul Mohiuddine
spellingShingle	Syed Abdul Mohiuddine Statistical weighted A-summability with application to Korovkin’s type approximation theorem Journal of Inequalities and Applications statistical convergence statistical weighted A-summability regular matrix positive linear operator Korovkin theorem
author_facet	Syed Abdul Mohiuddine
author_sort	Syed Abdul Mohiuddine
title	Statistical weighted A-summability with application to Korovkin’s type approximation theorem
title_short	Statistical weighted A-summability with application to Korovkin’s type approximation theorem
title_full	Statistical weighted A-summability with application to Korovkin’s type approximation theorem
title_fullStr	Statistical weighted A-summability with application to Korovkin’s type approximation theorem
title_full_unstemmed	Statistical weighted A-summability with application to Korovkin’s type approximation theorem
title_sort	statistical weighted a-summability with application to korovkin’s type approximation theorem
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2016-03-01
description	Abstract We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be weighted regular. As an application, we prove the Korovkin type approximation theorem through statistical weighted A-summability and using the BBH operator to construct an illustrative example in support of our result.
topic	statistical convergence statistical weighted A-summability regular matrix positive linear operator Korovkin theorem
url	http://link.springer.com/article/10.1186/s13660-016-1040-1
work_keys_str_mv	AT syedabdulmohiuddine statisticalweightedasummabilitywithapplicationtokorovkinstypeapproximationtheorem
_version_	1725882368078643200

Statistical weighted A-summability with application to Korovkin’s type approximation theorem

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