Fixed point results for generalized rectangular fuzzy b-metric-like spaces and applications

Abstract

This paper introduces a new extended rectangular fuzzy b-metric-like space that generalizes the existing frameworks of the extended rectangular and fuzzy b-metric spaces. Within this setting, we establish several fixed-point theorems for Ciric-type and Banach-type contractions, accompanied by a series of corollaries, propositions, and conditions that further illustrate the proposed concept. These results unify and extend many known theorems in fuzzy metric theory. Moreover, we provided several non-trivial examples to validate of the main results. A flow diagram was provided to demonstrate the generalized structure. Additionally, we applied the fuzzy integral equation to establish the uniqueness and existence of our main result.

Keywords

Fixed point / Operator equations / Hölderian / Nonlinear functional / Lipschitzian / Integral equations

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