Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for s...

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Autor principal:	Mualla Birgül Huban
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/221106d2ca884f989e0129bf69c2eabb
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id	oai:doaj.org-article:221106d2ca884f989e0129bf69c2eabb
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spelling	oai:doaj.org-article:221106d2ca884f989e0129bf69c2eabb2021-11-15T01:19:59ZLacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces2314-478510.1155/2021/7302292https://doaj.org/article/221106d2ca884f989e0129bf69c2eabb2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7302292https://doaj.org/toc/2314-4785The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ-invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ-invariant convergence Wℐσθη,ν (Wijsman sense), lacunary ℐ∗-invariant convergence Wℐσθ∗η,ν (Wijsman sense), and q-strongly lacunary invariant convergence WNσθη,νq (Wijsman sense) of sequences of sets in IFMS. Also, we give the relationships among Wijsman lacunary invariant convergence, WNσθη,νq, Wℐσθη,ν, and Wℐσθ∗η,ν in IFMS. Furthermore, we define the concepts of Wℐσθη,ν-Cauchy sequence and Wℐσθ∗η,ν-Cauchy sequence of sets in IFMS. Furthermore, we obtain some features of the new type of convergences in IFMS.Mualla Birgül HubanHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Mualla Birgül Huban Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces
description	The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ-invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ-invariant convergence Wℐσθη,ν (Wijsman sense), lacunary ℐ∗-invariant convergence Wℐσθ∗η,ν (Wijsman sense), and q-strongly lacunary invariant convergence WNσθη,νq (Wijsman sense) of sequences of sets in IFMS. Also, we give the relationships among Wijsman lacunary invariant convergence, WNσθη,νq, Wℐσθη,ν, and Wℐσθ∗η,ν in IFMS. Furthermore, we define the concepts of Wℐσθη,ν-Cauchy sequence and Wℐσθ∗η,ν-Cauchy sequence of sets in IFMS. Furthermore, we obtain some features of the new type of convergences in IFMS.
format	article
author	Mualla Birgül Huban
author_facet	Mualla Birgül Huban
author_sort	Mualla Birgül Huban
title	Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces
title_short	Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces
title_full	Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces
title_fullStr	Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces
title_full_unstemmed	Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces
title_sort	lacunary ℐ-invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/221106d2ca884f989e0129bf69c2eabb
work_keys_str_mv	AT muallabirgulhuban lacunaryiinvariantconvergenceofsequenceofsetsinintuitionisticfuzzymetricspaces
_version_	1718428910696267776

Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

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