# Fixed point theorems for $(\varepsilon,\lambda)$-uniformly locally contractive mapping defined on $\varepsilon$-chainable $G$-metric type spaces

## TL;DR

This paper establishes fixed point theorems for a class of locally contractive mappings on specialized metric spaces, extending existing results and introducing $\lambda$-sequences for new insights.

## Contribution

It generalizes fixed point results to $\varepsilon$-chainable $G$-metric spaces and introduces $\lambda$-sequences to derive novel fixed point theorems.

## Key findings

- Fixed point results hold under more general conditions.
- Extension of existing theorems to $\varepsilon$-chainable $G$-metric spaces.
- Introduction of $\lambda$-sequences for fixed point analysis.

## Abstract

In this article, we discuss fixed point results for $(\varepsilon,\lambda)$-uniformly locally contractive self mapping defined on $\varepsilon$-chainable $G$-metric type spaces. In particular, we show that under some more general conditions, certain fixed point results already obtained in the literature remain true. Moreover, in the last sections of this paper, we make use of the newly introduced notion of $\lambda$-sequences to derive new results.