Rectangular partial b-metric spaces

Abstract

In this article concept of rectangular partial b-metric space have been introduced. It is shown that rectangular b-metric can be achieved from rectangular partial b-metric. Moreover equivalence of completeness of both the spaces have been achieved. An analog to Cantor intersection theorem has been established in such spaces. A variant of Banach fixed point theorem and Kannan fixed point theorem are also proved in the language of rectangular partial b-metric spaces.