On M-Metric Space and Fixed Point Theorems.

Abstract

In this paper we make some observations concerning M−metric spaces and point out some discrepancies in some proofs found in the literature. To remedy this, we propose a new topolog- ical construction and prove that it is, in fact, a generalization of a partial metric space. Then, using this construction, we present our main theorem, having as its corollaries the fixed point theorems found in previous publications.