On$\mathfrak{R}$-Partial$b$-Metric Spaces and Related Fixed Point Results with Applications

Abstract

In this paper, we introduce the notion of R -partial b -metric spaces and prove some related fixed point results in the context of this notion. We also discuss an example to validate our result. Finally, as applications, we evince the importance of our work by discussing some fixed point results on graphical-partial b -metric spaces and on partially-ordered-partial b -metric spaces.