Multivalued Probabilistic ω-Contraction in b-Menger Spaces with Aapplication

In this article, we extend the concept of multivalued $\omega$-contraction mappings within the framework of b-Menger spaces. We introduce a novel fixed point theorem specific to these mappings, significantly broadening the existing body of knowledge in this area. Our primary result directly leads to the derivation of an equivalent fixed point theorem for fuzzy b-metric spaces, showcasing the versatility and applicability of our findings in more generalized and complex metric structures. Furthermore, we provide a concrete application of the principal theorem in the context of ordinary b-metric spaces, demonstrating the practical implications and effectiveness of our theoretical advancements. This research contributes to the deeper understanding and potential applications of fixed point theory in various scientific and engineering domains, where probabilistic and fuzzy structures play a critical role.