Best Proximity Point Results for Multi-Valued Mappings in Generalized Metric Structure

In this paper, we introduce the novel concept of generalized distance denoted as J theta 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 theta(u,H star), a generalized Hausdorff type distance and a PJ theta-property of a pair (H star,K star) of nonempty subsets of extended b-metric space (U star,rho theta). 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.