Coupled Coincidence Point Theorems for a $(\beta,g)$-$\psi$-Contractive Mapping in Partially Ordered $G$-Metric Spaces

P. Charoensawan, C. Thangthong

Abstract

In this paper, we introduce the notion $(\beta)$-admissible and $(\beta, g)$-admissible for mapping $F : X \times X \to X$ and  $g:X\to X$. We showed the existence of a coupled coincidence point theorem for a $(\beta,g)$-$\psi$-contractive mapping in $G$-metric spaces. We also show the uniqueness of a coupled common fixed point for such mappings and give some examples to show the validity of our result.