Coupled coincidence point theorems for a φ-contractive mapping in partially ordered G-metric spaces without mixed g-monotone property

Abstract

In this work, we show the existence of a coupled coincidence point and a coupled common fixed point for a φcontractive mapping in G-metric spaces without the mixed g-monotone property, using the concept of a (F*, g)-invariant set. We also show the uniqueness of a coupled coincidence point and give some examples, which are not applied to the existence of a coupled coincidence point by using the mixed g-monotone property. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mapping in partially ordered G-metric spaces. © 2014 Thangthong and Charoensawan; licensee Springer.