A fixed point theorem of Reich in \(G\)-Metric spaces

Zead Mustafa; Hamed Obiedat

doi:10.4067/S0719-06462010000100008

Authors

Zead Mustafa The Hashemite University, Department of Mathematics, P.O. Box 150459, Zarqa 13115, Jordan.
Hamed Obiedat The Hashemite University, Department of Mathematics, P.O. Box 150459, Zarqa 13115, Jordan.

DOI:

https://doi.org/10.4067/S0719-06462010000100008

Keywords:

Metric space, generalized metric space, D-metric space, 2-metric space

Abstract

In this paper we prove some fixed point results for mapping satisfying sufficient contractive conditions on a complete G-metric space, also we showed that if the G-metric space (X, G) is symmetric, then the existence and uniqueness of these fixed point results follows from Reich theorems in usual metric space (X, d_G), where (X, d_G) the metric induced by the G-metric space (X, G).