Sharp Best Proximity Point Results for Multivalued Operators in Extended Rectangular b-Metric Spaces

In this paper, we propose a novel extension of generalized distance, which we call the θ-extended rectangular b-generalized pseudo-distance. This new concept generalizes and unifies several known notions of distance by incorporating a parameter θ, along with the framework of rectangular b-metric spaces and pseudo-distances. The introduced structure is more flexible and capable of capturing a wider class of convergence and contractive behaviors in nonlinear analysis. Using this framework, we establish new best proximity point theorems for multivalued mappings of the Nadler type. These mappings are defined on θ-extended rectangular b-metric spaces, and the existence results are obtained under contractive-type conditions involving the newly defined pseudo-distance. Our results extend and generalize various existing fixed point and best proximity point theorems in the literature. Furthermore, we provide concrete and nontrivial examples to validate the theoretical findings. These examples illustrate the relevance and applicability of the proposed framework in dealing with problems where traditional metric assumptions may not hold. Our work opens new avenues for further exploration in metric fixed point theory, especially in settings involving generalized distance structures and multivalued analysis.