A NEW TYPE OF PARTIAL b-METRIC SPACE AND FIXED POINT THEOREMS

Abstract

In this study, we extend the concept of partial b-metric space to introduce Generalized partial b-metric space, building upon the work by S. Shukla in [25]. This new framework is motivated by the properties of partial b-metric spaces. We provide examples that illustrate scenarios not meeting the criteria of a partial b-metric space. Furthermore, our research includes the development and proof of several fixed point theorems. Notably, our findings generalize and expand upon various established results from existing literature.