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

Muhammad Rafique; Talat Nazir; Mujahid Abbas; Muhammad Rafique; Talat Nazir; Mujahid Abbas

doi:10.3934/math.2022125

AIMS Mathematics

2022, Volume 7, Issue 2: 2195-2219. doi: 10.3934/math.2022125

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Research article

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

1.
Department of Mathematics, COMSATS University Islamabad, Chak Shahzad, 44000 Islamabad, Pakistan
2.
Department of Mathematics, Huanghuai University, Zhumadian, Henan 463000, China
3.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
4.
Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
5.
Department of Medical research, China Medical University Hospital, China, Medical University, Taichung, Taiwan

Received: 07 September 2021 Accepted: 01 November 2021 Published: 10 November 2021
MSC : 47H10, 54H25

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.
- fuzzy set,
- fuzzy set-valued mapping,
- fuzzy fixed point,
- directed graph
Citation: Muhammad Rafique, Talat Nazir, Mujahid Abbas. Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph[J]. AIMS Mathematics, 2022, 7(2): 2195-2219. doi: 10.3934/math.2022125

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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.

References

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