Coincidence of Multivalued Mappings on Metric Spaces with a Graph

Abstract

In this article the coincidence points of a self mapping and a sequence of multivalued mappings are found using the graphic F-contraction inequality. This generalizes Mizoguchi-Takahashi’s fixed point theorem for multivalued mappings on a metric space endowed with a graph. As applications we obtain a theorem in homotopy theory, an existence theorem for the solution of a system of Urysohn integral equations, and for the solution of a special type of fractional integral equations.