Existence and data dependence of the fixed points of generalized contraction mappings with applications

Abstract

The aim of this paper is to introduce a new type of generalized multivalued contraction mappings and to present some results regarding fixed points of new class of multivalued contractions. As applications we obtain some basic results in fixed point theory like characterization of metric completeness, data dependence of fixed points and homotopy result. We prove the existence and uniqueness of bounded solution of functional equation arising in dynamic programming. Our results generalize, extend and unify various comparable results in the existing literature.