A characterization of E-completeness in vector metric spaces with an application in fixed point theory

Abstract

The main purpose of this article is to introduce the notion of dᵥ-point in a vector metric space which is a generalization of the notion of d-point in metric spaces and extend Weston’s characterization of metric completeness to vector metric spaces in terms of dᵥ-point. In fact, we have utilized the concepts of lower semicontinuity and uniform continuity in this new framework to establish the main result. Finally, we established relations among minimal points, dᵥ-points and fixed points in this new setting. As an application of this study, we obtained the analogue of Banach Contraction Principle in vector metric spaces.