Abstract
This article is concerned with a class of contractions in the framework of a fuzzy metric space endowed with a graph. The main results obtained not only broaden but also generalize a number of relevant results in the literature. Particularly, we get some results for cyclic contractions in fuzzy metric spaces. We also consider an integral equation.
Highlights
In recent years, fixed-point theory has become a tantalizing field of research in nonlinear analysis due to its wide range of applications in computer sciences, game theory, physics, economics, and various other fields
After the fundamental Banach’s theorem [3] in 1922, a huge amount of literature appeared for the investigation of fixed points of self-operators
E investigation of existence of a fixed point of selfmappings on a metric space (N, d) equipped with a partial ordering was originated by the works of Ran and Reurings [4]
Summary
In recent years, fixed-point theory has become a tantalizing field of research in nonlinear analysis due to its wide range of applications in computer sciences, game theory, physics, economics, and various other fields. Many authors undertook further advancements in this direction by generalizing the contraction inequalities and by providing the underlying space with rich geometric structure to make the results more viable In this context, recently a number of authors contributed new and exciting developments in fixed-point theory using fuzzy metric spaces; see [9,10,11,12,13,14,15,16,17,18] and the references included therein. E work of Jachymski motivated us to introduce the notion of fuzzy order κG-contractive mappings and study related fixed-point results in the context of a fuzzy metric space equipped with a graph. By a Journal of Mathematics successful application of our main result, we ensure the existence of a solution for an integral equation
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