Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

Abstract

nvolving w w -distances we prove a fixed point theorem of Caristi-type in the realm of (non-necessarily T 1 {T}_{1}) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non- T 1 {T}_{1} quasi-metric spaces. As an application, we deduce a characterization of complete G G -metric spaces in terms of a weak version of Caristi's theorem that involves a G-metric version of w-distances.