Coincidence point of L-fuzzy sets endowed with graph

Abstract

In the present paper, coincidence theorems of a crisp mapping and a sequence of L-fuzzy mappings have been produced under graphic contractive conditions in connection with notions of \(D_{\alpha _{L}}\) and \(d_{L}^{\infty }\) distances on the class of L-fuzzy sets. Further, we obtain some fixed point theorems for L-fuzzy set-valued mappings and pull out a variety of current results on fixed points for fuzzy mappings and multivalued mappings in the literature. As applications, we acquire coincidence points of a sequence of multivalued mappings with a self mapping and prove the existence of solution for fuzzy integral equations.