Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

We introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy...

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Main Authors:	Abdullah Alotaibi, Alaa Mohammed Aljahili, S.A. Mohiuddine
Format:	Article
Language:	English
Published:	Etamaths Publishing 2019-09-01
Series:	International Journal of Analysis and Applications
Online Access:	http://www.etamaths.com/index.php/ijaa/article/view/1867

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spelling	doaj-2633606142564561a5ccb21292f2244c2020-11-25T02:22:13ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392019-09-01175711721399Generalized Statistical Convergence of Double Sequences in Paranormed SpacesAbdullah Alotaibi0Alaa Mohammed Aljahili1S.A. Mohiuddine2King Abdulaziz UniversityKing Abdulaziz UniversityKing Abdulaziz UniversityWe introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy and strongly (λ, µ)p-summable double sequences in a paranormed space and obtain their relationship with (λ, µ)- statistical convergence.http://www.etamaths.com/index.php/ijaa/article/view/1867
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdullah Alotaibi Alaa Mohammed Aljahili S.A. Mohiuddine
spellingShingle	Abdullah Alotaibi Alaa Mohammed Aljahili S.A. Mohiuddine Generalized Statistical Convergence of Double Sequences in Paranormed Spaces International Journal of Analysis and Applications
author_facet	Abdullah Alotaibi Alaa Mohammed Aljahili S.A. Mohiuddine
author_sort	Abdullah Alotaibi
title	Generalized Statistical Convergence of Double Sequences in Paranormed Spaces
title_short	Generalized Statistical Convergence of Double Sequences in Paranormed Spaces
title_full	Generalized Statistical Convergence of Double Sequences in Paranormed Spaces
title_fullStr	Generalized Statistical Convergence of Double Sequences in Paranormed Spaces
title_full_unstemmed	Generalized Statistical Convergence of Double Sequences in Paranormed Spaces
title_sort	generalized statistical convergence of double sequences in paranormed spaces
publisher	Etamaths Publishing
series	International Journal of Analysis and Applications
issn	2291-8639
publishDate	2019-09-01
description	We introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy and strongly (λ, µ)p-summable double sequences in a paranormed space and obtain their relationship with (λ, µ)- statistical convergence.
url	http://www.etamaths.com/index.php/ijaa/article/view/1867
work_keys_str_mv	AT abdullahalotaibi generalizedstatisticalconvergenceofdoublesequencesinparanormedspaces AT alaamohammedaljahili generalizedstatisticalconvergenceofdoublesequencesinparanormedspaces AT samohiuddine generalizedstatisticalconvergenceofdoublesequencesinparanormedspaces
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Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

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