A new extension of the m-b-metric spaces

Abstract

In this paper, we present a new notion which is called an extended Mb-metric space as a generalization of an M-b-metric space. We investigate some basic and topological properties of this new space. Furthermore, an extended M-b-metric space is a new generalization of an M-metric space and partial metric space. So it is important to study fixed-point theorems for non-M -metric (or non-partial metric) functions on an extended M-b-metric space. Also we generalize some known results in literature.