In this manuscript, we establish some fixed point results for fuzzy mappings via -contractions. For validation of the proved results, some nontrivial examples are presented. Few interesting consequences are also stated which authenticate that our results generalize many existing ones in the literature.

Karapinar et al. established a more general class of contractions, namely, hybrid interpolative $\mathcal{R}$iech $\mathcal{I}$strǎstescue-type contractions, and presented some results on the platform of metric spaces. This research uses the domain of $\mathfrak{b}$-metric spaces to modify this class proficiently. Several interesting fixed-point results are presented by using this new class defined on $\mathfrak{b}$-metric space, where the symmetric condition is preserved in this study. Examples are provided for the authentication of proved results. Eventually, an application is also provided in order to comprehend our extensive effort in a better way.

Recently, Ji et al. established certain fixed-point results using Mann’s iterative scheme tailored to ${\mathcal{G}}_b$-metric spaces. Stimulated by the notion of the $\mathcal{F}$-contraction introduced by Wardoski, the contraction condition of Ji et al. was generalized in this research. Several fixed-point results with Mann’s iterative scheme endowed with $\mathcal{F}$-contractions in ${\mathcal{G}}_b$-metric spaces were proven. One non-trivial example was elaborated to support the main theorem. Moreover, for application purposes, the existence of the solution to an integral equation is provided by using the axioms of the proven result. The obtained results are generalizations of several existing results in the literature. Furthermore, the results of Ji. et al. are the special case of theorems provided in the present research.

This article contains results of the existence of fuzzy fixed points of fuzzy mappings that satisfy certain contraction conditions using the platform of partial b-metric spaces. Some non-trivial examples are provided to authenticate the main results. The constructed results in this work will likely stimulate new research directions in fuzzy fixed-point theory and related hybrid models. Eventually, some fixed-point results on multivalued mappings are established. These theorems provide an excellent application of main theorems on fuzzy mappings. The results of this article are extensions of many already existing results in the literature.

The present work is about the existence of best proximity points for Prešić type nonself operators in $ b $-metric spaces. In order to elaborate the results an example is presented. Moreover, some interesting formulations of Prešić fixed point results are also established. In addition a result in double controlled metric type space is also formulated.