Abstract
In the present paper, existence theorems of coincidence points of a crisp mapping and a sequence of L-fuzzy mappings have been established in a complete metric space under contractive type conditions in connection with newly defined notions of D-alpha L and d(L)(infinity) distances on the class of L-fuzzy sets. Furthermore, we obtain some fixed point theorems for L-fuzzy set-valued mappings to extend a variety of recent results on fixed points for fuzzy mappings and multivalued mappings in the literature. As applications, first we obtain coincidence points of a sequence of multivalued mappings with a self mapping and next established an existence and uniqueness theorem of the solution for a generalized class of nonlinear integral equations.