Fixed points of multivalued contractions in Hausdorff controlled metric spaces with applications

In this article, we introduce two multivalued contractive mappings within the framework of Hausdorff controlled metric spaces, employing concepts of admissibility and ‐class functions. The first mapping is a ‐generalized contractive multivalued mapping, and the second is a ‐multivalued mapping. We establish conditions guaranteeing the existence of fixed points for these mappings. To support our theoretical findings, we provide a numerical example, demonstrating the independence of the contractive conditions for the mappings. Furthermore, we apply our results to a specific problem in polynomial equations. These findings complement several existing results in the literature.