Coupled Coincidence Point Theorems for a \alpha-\psi-Contractive Mapping in Partially Metric Spaces with M-Invariant Set

Phakdi Charoensawan

Abstract

In this paper, we introduce the notion $M$-invariant set for mapping $\alpha : X ^2\times X^2 \to [0,+\infty)$. We showed the existence of a coupled coincidence point theorem for a $\alpha$-$\psi$-contractive mapping in partially ordered complete metric spaces without the mixed g-monotone property, using the concept of $M$-invariant set. 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.