($2k+1)^{th}$-order Fixed points in $G$-metric spaces

TL;DR

This paper proves new fixed-point theorems for functions with odd power contractive conditions in G-metric spaces, extending existing results to single, triplet, and family mappings.

Contribution

It introduces novel fixed-point theorems for odd power contractive functions in G-metric spaces, covering various mapping scenarios.

Findings

Established fixed-point theorems for single mappings

Extended results to triplet mappings

Generalized to families of mappings

Abstract

We establish three major fixed-point theorems for functions satisfying an odd power type contractive condition in G-metric spaces. We first consider the case of a single mapping, followed by that of a triplet of mappings and we conclude by the case of a family of mappings. The results we obtain in this article extend similar ones already present in the literature.