Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 181650, 9 pages
doi:10.1155/2010/181650
Research Article

Fixed Point Theory for Contractive Mappings Satisfying Φ-Maps in G-Metric Spaces

W. Shatanawi

Department of Mathematics, Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan

Received 23 March 2010; Revised 13 May 2010; Accepted 1 June 2010

Academic Editor: Brailey Sims

Copyright © 2010 W. Shatanawi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove some fixed point results for self-mapping T:X→X in a complete G-metric space X under some contractive conditions related to a nondecreasing map ϕ:[0,+∞)→[0,+∞) with limn→+∞ϕn(t)=0 for all t∈(0,+∞). Also, we prove the uniqueness of such fixed point, as well as studying the G-continuity of such fixed point.