A Unification of G -Metric, Partial Metric, and b -Metric Spaces

Abstract

Using the concepts of $G$-metric, partial metric, and $b$-metric spaces, we define a new concept of generalized partial $b$-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.