$n$-tuple fixed point in $\phi$-ordered $G$-metric spaces

TL;DR

This paper extends fixed point theory to $ $-tuple fixed points within $oldsymbol{ ext{G}}$-metric spaces, combining approaches from $G$-metrics, multidimensional fixed points, and partial orderings.

Contribution

It introduces new existence results for $n$-tuple fixed points in $oldsymbol{ ext{G}}$-metric spaces, generalizing previous quasi-pseudometric space results.

Findings

Existence of $n$-tuple fixed points in $oldsymbol{ ext{G}}$-metric spaces.

Extension of fixed point results to $oldsymbol{ ext{G}}$-metric setting.

Application to non-decreasing and weakly related mappings.

Abstract

We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces to the $G$-metric space setting. In particular, we show the existence of $n$-tuple fixed points (resp. common $n$-tuple fixed point) for a non-decreasing mapping (resp. a pair of weakly related mappings) in a $\phi$-ordered $G$-metric space.