Soft Limit and Soft Continuity

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dc.authorid0000-0002-1724-8841
dc.authorid0000-0001-7471-8486
dc.authorid0000-0002-7188-9893
dc.contributor.authorSapan, Kenan
dc.contributor.authorArslan, Burak
dc.contributor.authorEnginoglu, Serdar
dc.date.accessioned2026-02-03T12:00:02Z
dc.date.available2026-02-03T12:00:02Z
dc.date.issued2025
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractThis study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano's theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed.
dc.identifier.doi10.3390/appliedmath5020065
dc.identifier.issn2673-9909
dc.identifier.issue2
dc.identifier.scopus2-s2.0-105009263810
dc.identifier.scopusqualityQ3
dc.identifier.urihttps://doi.org/10.3390/appliedmath5020065
dc.identifier.urihttps://hdl.handle.net/20.500.12428/34485
dc.identifier.volume5
dc.identifier.wosWOS:001515081500001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofAppliedmath
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20260130
dc.subjectsoft sets
dc.subjectsoft analysis
dc.subjectsoft limit
dc.subjectsoft continuity
dc.titleSoft Limit and Soft Continuity
dc.typeArticle

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