Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems

Abstract The concept of deferred Nörlund equi-statistical convergence has recently been studied by Srivastaval et al. (see,[19]). In this paper, we have introduced the notion of equi-statistical convergence, statistical point-wise convergence and statistical uniform convergence in conjunction with t...

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Autores principales:	Parida,P., Paikray,S. K., Jena,B. B.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Statistical convergence Cesàro deferred convergene Deferred equi-statistical convergence Rate of convergence Korovkin-type approximation theorems Banach space and positive linear operator
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200317
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spelling	oai:scielo:S0716-091720200002003172020-05-06Generalized deferred Cesàro equi-statistical convergence and analogous approximation theoremsParida,P.Paikray,S. K.Jena,B. B. Statistical convergence Cesàro deferred convergene Deferred equi-statistical convergence Rate of convergence Korovkin-type approximation theorems Banach space and positive linear operator Abstract The concept of deferred Nörlund equi-statistical convergence has recently been studied by Srivastaval et al. (see,[19]). In this paper, we have introduced the notion of equi-statistical convergence, statistical point-wise convergence and statistical uniform convergence in conjunction with the deferred statistical convergence and established a inclusion relation between them. Moreover, we have applied our idea (presumably new) of the deferred equi-statistical convergence to prove a Korovkin-type approximation theorem and demonstrated that our theorem is a non-trivial extension of some well-established Korovkintype approximation theorems which ware proved by some earlier authors. Furthermore, we have established the rate of deferred equistatistical convergence and accordingly proved a theorem. Finally, some concluding remarks and fascinating cases are shown here in support of our definitions and results.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.2 20202020-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200317en10.22199/issn.0717-6279-2020-02-0020
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Statistical convergence Cesàro deferred convergene Deferred equi-statistical convergence Rate of convergence Korovkin-type approximation theorems Banach space and positive linear operator
spellingShingle	Statistical convergence Cesàro deferred convergene Deferred equi-statistical convergence Rate of convergence Korovkin-type approximation theorems Banach space and positive linear operator Parida,P. Paikray,S. K. Jena,B. B. Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
description	Abstract The concept of deferred Nörlund equi-statistical convergence has recently been studied by Srivastaval et al. (see,[19]). In this paper, we have introduced the notion of equi-statistical convergence, statistical point-wise convergence and statistical uniform convergence in conjunction with the deferred statistical convergence and established a inclusion relation between them. Moreover, we have applied our idea (presumably new) of the deferred equi-statistical convergence to prove a Korovkin-type approximation theorem and demonstrated that our theorem is a non-trivial extension of some well-established Korovkintype approximation theorems which ware proved by some earlier authors. Furthermore, we have established the rate of deferred equistatistical convergence and accordingly proved a theorem. Finally, some concluding remarks and fascinating cases are shown here in support of our definitions and results.
author	Parida,P. Paikray,S. K. Jena,B. B.
author_facet	Parida,P. Paikray,S. K. Jena,B. B.
author_sort	Parida,P.
title	Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
title_short	Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
title_full	Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
title_fullStr	Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
title_full_unstemmed	Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
title_sort	generalized deferred cesàro equi-statistical convergence and analogous approximation theorems
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200317
work_keys_str_mv	AT paridap generalizeddeferredcesaroequistatisticalconvergenceandanalogousapproximationtheorems AT paikraysk generalizeddeferredcesaroequistatisticalconvergenceandanalogousapproximationtheorems AT jenabb generalizeddeferredcesaroequistatisticalconvergenceandanalogousapproximationtheorems
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Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems

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