Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems

In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the idea of statistical convergence for sequences of real numbers, which are defined over a Banach space via the product of deferred Cesàro and deferred weigh...

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Autor principal:	Bidu Bhusan Jena , Susanta Kumar Paikray
Formato:	article
Lenguaje:	EN ES
Publicado:	Pontificia Universidad Javeriana 2020
Materias:	statistical convergence; statistical probability convergence; deferred cesàro and deferred weighted product mean; positive linear op-erators; sequence of random variables; banach space; korovkin-type theo-rems; rate of statistical probability convergence. Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/d6f72a7c4679468d982d0241d6a2b3a7
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spelling	oai:doaj.org-article:d6f72a7c4679468d982d0241d6a2b3a72021-11-17T13:47:13ZProduct of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems10.11144/Javeriana.SC25-3.podc0122-74832027-1352https://doaj.org/article/d6f72a7c4679468d982d0241d6a2b3a72020-10-01T00:00:00Zhttps://revistas.javeriana.edu.co/index.php/scientarium/article/view/27314https://doaj.org/toc/0122-7483https://doaj.org/toc/2027-1352In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the idea of statistical convergence for sequences of real numbers, which are defined over a Banach space via the product of deferred Cesàro and deferred weighted summability means. We first establish a theorem presenting aconnection between them. Based upon our proposed methods, we then prove a Korovkin-type approximation theorem with algebraic test functions for a sequence of random variables on a Banach space, and demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results (in classical as well as in statistical versions). Furthermore, an illustrative example is presented here by means of the generalized Meyer–König and Zeller operators of a sequence of random variables in order to demonstrate that our established theorem is stronger than its traditional and statistical versions. Finally, we estimate the rate of the product of deferred Cesàro and deferred weighted statistical probability convergence, and accordingly establish a new result. Bidu Bhusan Jena , Susanta Kumar PaikrayPontificia Universidad Javerianaarticlestatistical convergence; statistical probability convergence; deferred cesàro and deferred weighted product mean; positive linear op-erators; sequence of random variables; banach space; korovkin-type theo-rems; rate of statistical probability convergence.Science (General)Q1-390ENESUniversitas Scientiarum, Vol 25, Iss 3, Pp 409-433 (2020)
institution	DOAJ
collection	DOAJ
language	EN ES
topic	statistical convergence; statistical probability convergence; deferred cesàro and deferred weighted product mean; positive linear op-erators; sequence of random variables; banach space; korovkin-type theo-rems; rate of statistical probability convergence. Science (General) Q1-390
spellingShingle	statistical convergence; statistical probability convergence; deferred cesàro and deferred weighted product mean; positive linear op-erators; sequence of random variables; banach space; korovkin-type theo-rems; rate of statistical probability convergence. Science (General) Q1-390 Bidu Bhusan Jena , Susanta Kumar Paikray Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
description	In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the idea of statistical convergence for sequences of real numbers, which are defined over a Banach space via the product of deferred Cesàro and deferred weighted summability means. We first establish a theorem presenting aconnection between them. Based upon our proposed methods, we then prove a Korovkin-type approximation theorem with algebraic test functions for a sequence of random variables on a Banach space, and demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results (in classical as well as in statistical versions). Furthermore, an illustrative example is presented here by means of the generalized Meyer–König and Zeller operators of a sequence of random variables in order to demonstrate that our established theorem is stronger than its traditional and statistical versions. Finally, we estimate the rate of the product of deferred Cesàro and deferred weighted statistical probability convergence, and accordingly establish a new result.
format	article
author	Bidu Bhusan Jena , Susanta Kumar Paikray
author_facet	Bidu Bhusan Jena , Susanta Kumar Paikray
author_sort	Bidu Bhusan Jena , Susanta Kumar Paikray
title	Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
title_short	Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
title_full	Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
title_fullStr	Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
title_full_unstemmed	Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
title_sort	product of deferred cesàro and deferred weighted statistical probability convergence and its applications to korovkin-type theorems
publisher	Pontificia Universidad Javeriana
publishDate	2020
url	https://doaj.org/article/d6f72a7c4679468d982d0241d6a2b3a7
work_keys_str_mv	AT bidubhusanjenasusantakumarpaikray productofdeferredcesaroanddeferredweightedstatisticalprobabilityconvergenceanditsapplicationstokorovkintypetheorems
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Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems

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