COINCIDENCE POINT THEOREMS IN HIGHER DIMENSION FOR NONLINEAR CONTRACTIONS

Abstract

In this manuscript, we introduce the concept of a coincidence point of $N$-order of $F : X^N \rightarrow X$ and $g : X \rightarrow X$ where $N\geq 2$ and $X$ is an ordered set endowed with a metric $d$. We prove some coincidence point theorems of such mappings involving nonlinear contractions. The presented results are generalizations of the recent fixed point theorems due to Berzig and Samet [M. Berzig and B. Samet, An extension of coupled fixed point's concept in higher dimension and applications, Comput. Math. Appl. 63 (2012) 1319--1334]. Also, this work is an extension of M. Borcut [M. Borcut, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput. 218 (2012) 7339--7346].