Partial n-metric spaces and fixed point theorems

TL;DR

This paper introduces partial n-metric spaces, a unified framework generalizing several metric space concepts, and establishes fixed point theorems within this new structure.

Contribution

It combines partial metric, G-metric, and n-metric spaces into a single generalized structure and proves fixed point theorems for these spaces.

Findings

Established Cauchy mapping theorems in partial n-metric spaces

Proved fixed point theorems for the new structure

Unified various metric space concepts into one framework

Abstract

In this paper we combine the notions of partial metric spaces with negative distances, $G_p$-metric spaces and n-metric spaces together into one structure called the partial n-metric spaces. These are generalizations of all the said structures, and also generalize the notions of $G$-metric and $G_p$-metric spaces to arbitrary finite dimension. We prove Cauchy mapping theorems and other fixed point theorems for such spaces.