This article is cited in 2 papers

Fixed points of fuzzy multivalued $F$-contractive mappings with a directed graph in parametric metric spaces

M. Rafique^a, T. Nazir^b, H. Kalita<sup>c

a</sup> Department of Mathematics, COMSATS University Islamabad, 44000, Pakistan
^b Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa
^c Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Bhopal-Indore Highway, Kothrikalan, Sehore, Madhya Pradesh, India

Abstract: In the structure of a parametric metric space accompanied by directed graph, we introduce the idea of fuzzy multivalued $F$-contractive mappings. Results related to the existence of common fuzzy fixed points are introduced. The proved results are supported by an example. Our results bring together, sum up, and supplement different familiar related results in the literature. We hope that the acclaimed results in our work will encourage new analysis aspects in fixed-point theory and parallel hybrid models in the literature of fuzzy mathematics supplemented with a graph.

Keywords: $F$-contraction, fuzzy set, fuzzy multivalued mapping, fuzzy fixed point.

UDC: 517.98

MSC: 46S40, 47H10, 54H25

Received: 21.03.2024
Revised: 05.06.2024
Accepted: 03.06.2024

Language: English

DOI: 10.15393/j3.art.2024.15870