Coincidence of crisp and fuzzy functions

Abstract_ _ We prove a common coincidence point theorem for a non-fuzzy mapping and a pair of fuzzy mappings under a ' contraction condition on a metric space in the context of Hausdor¤ metric on the family of fuzzy sets. Further, we establish a common coincidence point theorem on a metric space with the d1 metric on fuzzy sets, which extends a number of recent results. As applications, we obtain a common coincidence point theorem for a single valued mapping and a pair of set-valued mappings and apply it to achieve some existence and uniqueness theorems of solution for a class of nonlinear integral equations. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2010 Mathematics Subject Classi…cation: 46S40; 47H10; 54H25.