Generalized Ćirić-Reich-Rus Contractions for Multivalued Mappings in Weighted ψ-b-Metric Spaces with Numerical Applications

This paper introduces groundbreaking fixed point and best proximity point results for multivalued mappings within the innovative framework of weighted ψ-b-metric spaces, addressing a significant gap in contemporary metric fixed point theory. We establish a novel and comprehensive fixed point theorem under a sophisticated generalized contractive condition of Reich–Rus–Ćirić type, uniquely incorporating both control functions and weight functions to achieve unprecedented theoretical depth. Our main contribution features an elegant synthesis of proximity point theory with weighted metric structures, providing a powerful analytical tool that transcends traditional metric limitations. Carefully constructed numerical examples demonstrate the practical applicability and theoretical robustness of our main theorems with applications to numerical examples. The obtained results represent a substantial advancement that not only unifies but significantly extends numerous classical theorems in the literature, opening new avenues for research in fixed point theory and their diverse applications across mathematical analysis.