Knaster-Kuratowski-Mazurkiewicz Theorem in Generalized Metric Spaces with Applications

Abstract

We study Knaster-Kuratowski-Mazurkiewicz theorem in the setting of generalized metric spaces. We establish some results on fixed points of Knaster-Kuratowski-Mazurkiewicz (KKM) mappings. Fan’s matching and Schauder’s type fixed point theorem in generalized metric spaces are also proved as interesting consequences of our main results. Examples are given to validate our results. We use these results to prove existence result for a given Atangana-Baleanu-Caputo fractional boundary value problem.