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In this paper, we introduce the novel concept of generalized distance denoted as J θ and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance J θ (u , H ★) , a generalized Hausdorff type distance and a P J θ -property of a pair (H ★ , K ★) of nonempty subsets of extended b-metric space (U ★ , ρ θ). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to prove some new fixed-point results for the two families of multivalued dominated-contractive maps defined on a closed ball in a complete multiplicative-metric space. The fixed-point theorems for multigraph-dominated maps are established. We also investigate the existence of fixed points of the two families of graphic contractions in a multiplicative-metric space. For illustration, an example is provided to clarify that the hypothesis of the obtained result is valid. Moreover, the applications of the obtained results to show the existence of solutions to the coupled systems of nonlinear Volterra-type integral equations and mappingal equations are presented as a confirmation of the novelty of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation's solution. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce a new motif of α ∗ -ψ-Λ-contraction multivalued mappings, some novel fixed-point and coincidence-point results for this contraction will be investigated in the scope of F-metric spaces, and some examples are given to illustrate our main results and we derive the existence and uniqueness of a solution of a functional equation to support our main result. [ABSTRACT FROM AUTHOR]

The manuscript is an extension of the investigations concerning θ-contractions which have been newly proposed in (Jleli and Samet in J. Inequal. Appl. 2014:38, 2014). The authors generalize the notion of θ-contractions to the case of nonlinear θ b -contraction mappings and prove multi-valued fixed point theorems based on the b-Bianchini–Grandolfi gauge function in b-metric spaces. The manuscript consists of a tangible example which displays the motivation for such investigations. The work is compiled by the application of the proposed nonlinear θ b -contractions to Liouville–Caputo fractional differential equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish Ćirić type fixed point results for multi-valued mappings satisfying generalized α-ψ-contractive conditions on closed ball in complete metric space. As an application, we derive some new fixed point theorems for Ćirić type ψ-graphic contractions and rational - graphic contractions defined on metric space endowed with a graph as well as ordered metric space. Examples has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish fixed point results for semi fixed α*-admissible multivalued mappings satisfying generalized locally α*-ψ-contractive conditions in complete dislocated metric space. As an application, we derive some new fixed point theorems for preordered metric space and metric space endowed with a graph. Example has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several comparable results in the existing literature. [ABSTRACT FROM AUTHOR]