Some results on a tripled fixed point for nonlinear contractions in partially ordered G-metric spaces

Abstract

Berinde and Borcut (Nonlinear Anal. 74(15):4889-4897, 2011) have quite recently defined the notion of a triple fixed point and proved some interesting results related to this concept in a partially ordered metric space. In this work we prove some triple fixed point theorem for a mixed monotone mapping satisfying nonlinear contractions in the framework of a generalized metric space endowed with partial order while the idea of a generalized metric space introduced by Mustafa and Sims (J. Nonlinear Convex Anal. 7:289-297, 2006). Further we prove the uniqueness of a coupled fixed point for such a mapping in this setting. © 2012 Mohiuddine and Alotaibi; licensee Springer.