On D-b-metric and general partial b-metric spaces

Abstract EN

In this paper, we introduce a new type of generalize metric space, which we call -metric space as a generalization of both -metric and b-metric spaces.

Then we prove some fixed point theorem in this space.

Also we define a general partial b-metric space as a generalize of a partial b-metric space and study their properties.

Finally, find relation between partial b-metric, -metric and general partial b-metric spaces.