Some set-valued and multi-valued contraction results in fuzzy cone metric spaces

This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-va...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 19
Main Authors Rehman, Saif Ur, Aydi, Hassen, Chen, Gui-Xiu, Jabeen, Shamoona, Khan, Sami Ullah
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.06.2021
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Contraction conditions
Fixed point
Fixed points (mathematics)
Fuzzy cone metric space
Fuzzy sets
Hausdorff metric
Mathematics
Mathematics and Statistics
Metric space
Neighborhoods
Theorems
Contraction conditions
47H10
Fuzzy cone metric space
Hausdorff metric
Fixed point
54H25
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Summary:This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-valued rational type fuzzy cone-contractions in fuzzy cone metric spaces. Our results extend and improve some results given in the literature.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02646-3