Coincidence of Multivalued Mappings on Metric Spaces with a Graph

Muhammad Nouman Aslam Khan, Akbar Azam, Ljubisa D.R. Kocinac


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.

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