In this paper, we initiate the notion of generalized multivalued ( α K * , Υ , Λ ) -contractions and provide some new common fixed point results in the class of α K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

In this paper, by characterizing a weak contractive condition based on using C − functions and α − admissible multi-valued mapping of type S, we present some fixed point results for ( α , F ) − admissible multi-valued mappings in the setting of b − metric spaces. Some examples and an application are added in order to show the reliability of our obtained results. Our results amend, unify, and generalize some existing results in the literature. The scientific novelty of our main results is to take new contraction self-mappings in b − metric spaces for multi-valued mappings.

In this paper, we introduce the notation of (α − η) − (ψ − ϕ)-contraction mappings defined on a set X. We prove the existence of common fixed point results for the pair of self-mappings involving C-class functions in the setting of metric space. Our results generalize and extend several works existing in literature. We provide an example and some applications in order to support our results.

In this paper, we prove some new fixed and common fixed point results in the framework of partially ordered quasi-metric spaces under linear and nonlinear contractions. Also we obtain some fixed point results in the framework of G-metric spaces.

The aim of this manuscript is to introduce the concept of fuzzy b-metric-like spaces and discuss some related fixed point results. Some examples are imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the obtained results, an application is provided to solve a first kind of Fredholm type integral equations.