Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

Muhammad Rafique; Talat Nazir; Mujahid Abbas

doi:10.3934/math.2022125

Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

Muhammad Rafique
, Talat Nazir
, Mujahid Abbas

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a new class of generalized graphic fuzzy F-contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.

Original language	English
Pages (from-to)	2195-2219
Number of pages	25
Journal	AIMS Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/math.2022125
Publication status	Published - 2022
Externally published	Yes

Keywords

Directed graph
Fuzzy fixed point
Fuzzy set
Fuzzy set-valued mapping

ASJC Scopus subject areas

General Mathematics

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10.3934/math.2022125

Cite this

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abstract = "We introduce a new class of generalized graphic fuzzy F-contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.",

keywords = "Directed graph, Fuzzy fixed point, Fuzzy set, Fuzzy set-valued mapping",

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AU - Nazir, Talat

AU - Abbas, Mujahid

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N2 - We introduce a new class of generalized graphic fuzzy F-contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.

AB - We introduce a new class of generalized graphic fuzzy F-contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.

KW - Directed graph

KW - Fuzzy fixed point

KW - Fuzzy set

KW - Fuzzy set-valued mapping

UR - https://www.scopus.com/pages/publications/85118626318

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DO - 10.3934/math.2022125

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JF - AIMS Mathematics

IS - 2

ER -

Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

Abstract

Keywords

ASJC Scopus subject areas

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