# New fixed point results on $G$-metric spaces

## TL;DR

This paper presents new fixed point theorems for contractive self mappings in $G$-metric spaces, focusing on mappings with contractive iterates at a point, expanding the theoretical understanding of such spaces.

## Contribution

It introduces novel fixed point results specifically for mappings with contractive iterates in $G$-metric spaces, which were not previously established.

## Key findings

- Established fixed point theorems for contractive mappings with iterates at a point
- Extended fixed point theory within the framework of $G$-metric spaces
- Provided conditions under which fixed points exist in this setting

## Abstract

In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point.