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

Abstract

Involving ww-distances we prove a fixed point theorem of Caristi-type in the realm of (non-necessarily T1{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-T1{T}_{1} quasi-metric spaces. As an application, we deduce a characterization of complete GG-metric spaces in terms of a weak version of Caristi’s theorem that involves a G-metric version of w-distances.

Keywords

• quasi-metric
• complete
• w-distance
• fixed point
• g-metric
• 47h10
• 54h25
• 54e50