Periodic Points of Weaker Meir-Keeler Contractive Mappings on Generalized Quasimetric Spaces

Abstract

By using the weaker Meir-Keeler function $\varphi$ and the triangular $\alpha$-admissible mapping $\alpha$, we introduce the notion of $(\alpha -\varphi )$-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.