Existence of Periodic Fixed Point Theorems in the Setting of Generalized Quasi-Metric Spaces

Abstract

We introduce the notions of $(\alpha -\varphi -\psi )$-weaker Meir-Keeler contractive mappings and $(\alpha -\phi )$-stronger Meir-Keeler contractive mappings. We discuss the existence of periodic points in the setting of generalized quasi-metric spaces. Our results improve, extend, and generalize several results in the literature.