Fixed point theorems for weak contraction in partially ordered G-metric space

TL;DR

This paper extends fixed point theorems to partially ordered G-metric spaces using $(,)$-weak contraction, demonstrating that these results differ from classical metric space theorems through examples.

Contribution

It introduces new fixed point theorems in G-metric spaces with partial order, expanding the scope of existing contraction principles.

Findings

Extended fixed point theorems to G-metric spaces with partial order.

Provided examples showing non-equivalence to classical metric space results.

Demonstrated the applicability of the theorems through specific cases.

Abstract

In this article, we present some fixed point theorems in partially ordered G-metric space using the concept of $(\psi,\phi)$- weak contraction which extend many existing fixed point theorems in such space. We also give some examples to show that if we transform a metric space into a G-metric space our results are not equivalent to the existing results in metric space.