Abstract
In this article, the concept of extended fuzzy rectangular b-metric space (EFRbMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFRbMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed.
Highlights
Motivated by the works [20,24], we introduce the notion of extended fuzzy rectangular b-metric space (EFRb MS) and establish some fixed point results via α-admissibility in the setting of EFRb MS
Our notions and results generalize some other concepts and fixed point results existing in the literature for fuzzy metric spaces
By pursuing the idea of fuzzy rectangular b-metric space presented by Mehmood et al [20], we introduce the notion of extended fuzzy rectangular b-metric space and generalize some fixed point results via α-η-β contractions
Summary
In 1965, Zadeh [1] introduced the concept of fuzzy set and fuzzy logic, providing a new context as an extension of the classical sets and logic. An element either does or does not belong to a set under consideration, whereas, in the fuzzy logic, the bonding of an element to a set is expressed as a real number from the interval [0, 1]. Since the establishment of this setting, a substantial number of pieces of literature have been developed in order to gain insight into the theory of fuzzy sets and their applications. Heilpern [2] introduced the concept of fuzzy mapping and provided some fixed point results for this type of mappings
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