A fixed point theorem in strictly convex $ b $-fuzzy metric spaces

The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $ b $-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $ b $-fuzzy metric spac...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 9; pp. 20989 - 21000
Main Authors Ješić, Siniša N., Ćirović, Nataša A., Nikolić, Rale M., Ranƌelović, Branislav M.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
b $-fuzzy metric spaces
convex structure
fixed point
normal structure
strictly convex structure
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Summary:The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $ b $-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $ b $-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $ b $-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231068