Existence of solutions to multivalued problems in incomplete metric spaces with applications

Abstract

. In this paper, we obtain some existence results for multivalued contraction mappings in the context of an O-complete orthogonal metric space (not necessarily complete metric space). Also, we provide a partial solution to Reich’s problem for multivalued orthogonal contraction mappings and extend Mizoguchi-Takahashi’s point theorem. In addition, we give an example to demonstrate the applicability of our established results. We study the solution of a differential equation and its Ulam’s stability as an application of the obtained results.