Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces

Shazia Kanwal; Asif Ali; Abdullah Al Mazrooei; Gustavo Santos-Garcia; Shazia Kanwal; Asif Ali; Abdullah Al Mazrooei; Gustavo Santos-Garcia

doi:10.3934/math.2023511

AIMS Mathematics

2023, Volume 8, Issue 5: 10095-10112. doi: 10.3934/math.2023511

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Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces

1.
Department of Mathematics, Government College University Faisalabad, Pakistan
2.
Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 80203, Saudi Arabia
3.
IME, Universidad de Salamanca, Spain

Received: 22 September 2022 Revised: 28 November 2022 Accepted: 04 December 2022 Published: 24 February 2023
MSC : 46S40, 47H10, 54H25

A contemporary fuzzy technique is employed in the current study to generalize some established and recent findings. For researchers, fixed point (FP) procedures are highly advantageous and appealing mechanisms. Discovering fuzzy fixed points of fuzzy mappings (FM) meeting Nadler's type contraction in complete fuzzy metric space (FMS) and?iri? type contraction in complete metric spaces (MS) is the core objective of this research. The outcomes are backed up by example and applications that highlight these findings. There are also preceding conclusions that are given as corollaries from the relevant literature. In this mode, numerous consequences exist in the significant literature are extended and combined by our findings.
- fuzzy metric space,
- fuzzy fixed point,
- fuzzy mapping,
- Hausdorff metric space,
- Hausdorff fuzzy metric space
Citation: Shazia Kanwal, Asif Ali, Abdullah Al Mazrooei, Gustavo Santos-Garcia. Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces[J]. AIMS Mathematics, 2023, 8(5): 10095-10112. doi: 10.3934/math.2023511

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Abstract

A contemporary fuzzy technique is employed in the current study to generalize some established and recent findings. For researchers, fixed point (FP) procedures are highly advantageous and appealing mechanisms. Discovering fuzzy fixed points of fuzzy mappings (FM) meeting Nadler's type contraction in complete fuzzy metric space (FMS) and?iri? type contraction in complete metric spaces (MS) is the core objective of this research. The outcomes are backed up by example and applications that highlight these findings. There are also preceding conclusions that are given as corollaries from the relevant literature. In this mode, numerous consequences exist in the significant literature are extended and combined by our findings.

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