The aim of this paper is to introduce a newtype 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.