Existence and Uniqueness of Fixed Points for Multivalued Mappings in Complete Metric Spaces

This paper investigates the existence and uniqueness of fixed points for multivalued mappings in complete metric spaces. We introduce a new class of contractive conditions for multivalued mappings and establish fixed point theorems that generalize several classical results. Our approach relies on the Hausdorff metric and a novel auxiliary function that characterizes the contraction properties. The theoretical framework developed here extends previous work by weakening certain assumptions while maintaining the essential characteristics needed for fixed point guarantees. Applications to integral inclusions and differential equations are discussed, highlighting the practical significance of the results.