Double-Controlled Quasi <i>M</i>-Metric Spaces

Abstract

One of the well-studied generalizations of a metric space is known as a partial metric space. The partial metric space was further generalized to the so-called M-metric space. In this paper, we introduce the Double-Controlled Quasi M-metric space as a new generalization of the M-metric space. In our new generalization of the M-metric space, the symmetry condition is not necessarily satisfied and the triangle inequality is controlled by two binary functions. We establish some fixed point results, along with the examples and applications to illustrate our results.

Keywords

• quasi-metric space
• partial metric space
• M-metric space
• Double-Controlled Quasi M-metric spaces
• fixed point theorem