ON [I.sub.[DELTA]]-DEFERRED STATISTICALLY ROUGH CONVERGENCE WITH ORDER [alpha]

In this article, we introduce the concept of [I.sub.[DELTA]]-deferred statistically rough convergence of order [alpha], (0 < [alpha] [less than or equal to] 1) in a normed linear space. We mainly examine various properties such as closedness and convexity of the set of I - [DS.sub.p,q.sup.r,[alph...

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Published inTWMS journal of applied and engineering mathematics Vol. 14; no. 4; p. 1526
Main Authors Choudhury, C, Kucukaslan, M
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.09.2024
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Abstract In this article, we introduce the concept of [I.sub.[DELTA]]-deferred statistically rough convergence of order [alpha], (0 < [alpha] [less than or equal to] 1) in a normed linear space. We mainly examine various properties such as closedness and convexity of the set of I - [DS.sub.p,q.sup.r,[alpha]] ([DELTA])--limit for a sequence. Besides this, we prove a necessary and sufficient condition for the I - [DS.sub.p,q.sup.r,[alpha]]([DELTA])--convergence of a real valued sequence and derive some interesting implication relationships. Keywords: Deferred statistical convergence, ideal, I--convergence, difference of sequence, rough convergence. AMS Subject Classification (2020): 40A35, 40A05.
AbstractList In this article, we introduce the concept of [I.sub.[DELTA]]-deferred statistically rough convergence of order [alpha], (0 < [alpha] [less than or equal to] 1) in a normed linear space. We mainly examine various properties such as closedness and convexity of the set of I - [DS.sub.p,q.sup.r,[alpha]] ([DELTA])--limit for a sequence. Besides this, we prove a necessary and sufficient condition for the I - [DS.sub.p,q.sup.r,[alpha]]([DELTA])--convergence of a real valued sequence and derive some interesting implication relationships.
In this article, we introduce the concept of [I.sub.[DELTA]]-deferred statistically rough convergence of order [alpha], (0 < [alpha] [less than or equal to] 1) in a normed linear space. We mainly examine various properties such as closedness and convexity of the set of I - [DS.sub.p,q.sup.r,[alpha]] ([DELTA])--limit for a sequence. Besides this, we prove a necessary and sufficient condition for the I - [DS.sub.p,q.sup.r,[alpha]]([DELTA])--convergence of a real valued sequence and derive some interesting implication relationships. Keywords: Deferred statistical convergence, ideal, I--convergence, difference of sequence, rough convergence. AMS Subject Classification (2020): 40A35, 40A05.
Audience Academic
Author Kucukaslan, M
Choudhury, C
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Title ON [I.sub.[DELTA]]-DEFERRED STATISTICALLY ROUGH CONVERGENCE WITH ORDER [alpha]
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