A CHARACTERIZATION OF E-COMPLETENESS IN VECTOR METRIC SPACES WITH AN APPLICATION IN FIXED POINT THEORY

A CHARACTERIZATION OF E-COMPLETENESS IN VECTOR METRIC SPACES WITH AN APPLICATION IN FIXED POINT THEORY

S. Kumar Mohanta, S. Das

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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.

Keywords

dv-point, E-completeness, minimal point, fixed point.