In this paper, by introducing the concept of a fuzzy rectangular- b -metric space, the notion of a fuzzy metric space and a fuzzy b -metric space are generalized. The well known metric fixed point theorems are established in the setting of fuzzy rectangular b -metric spaces and illustrated by examples. To show the significance of our result an application is presented to establish the existence of a solution of integral equation. Our results generalize many existing theorems in the literature.

In this paper, we study the notion of a fuzzy b-metric space and establish certain fixed point results for Geraghty-type contraction in the setting of G-complete fuzzy b-metric space. We furnish an example to illustrate our main result. Our results extend and generalize the existing results in the literature. An application related to our main result for the existence of solution of nonlinear integral equations is also presented.

In this article, the notion of Hausdorff fuzzy $ b $-metric space is studied. Some fixed point results for multivalued mappings using Geraghty type contractions in $ G $-complete fuzzy $ b $-metric spaces are established. To strengthen the results, an illustrative example is furnished. A fuzzy integral inclusion is constructed as an application of fixed point result which shows the validity of the proved results. The presented outcomes are the generalization of the existing results in literature.