The property of presymmetry for $w$-distances on quasi-metric spaces

Abstract

In this paper we extend the recently introduced notion of presymmetric $w$-distance on metric spaces to the context of quasi-metric spaces. We establish some of its properties and present various examples. We also show that this notion provides an efficient setting to obtain a suitable and large quasi-metric extension of a nice and elegant generalization of Banach’s contraction principle due to Suzuki.