Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 657914, 10 pages
doi:10.1155/2009/657914
Review Article

Some Generalizations of Fixed Point Theorems in Cone Metric Spaces

J. O. Olaleru

Mathematics Department, University of Lagos, Yaba, Lagos, Nigeria

Received 17 March 2009; Revised 15 July 2009; Accepted 29 August 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2009 J. O. Olaleru. 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 generalize, extend, and improve some recent fixed point results in cone metric spaces including the results of H. Guang and Z. Xian (2007); P. Vetro (2007); M. Abbas and G. Jungck (2008); Sh. Rezapour and R. Hamlbarani (2008). In all our results, the normality assumption, which is a characteristic of most of the previous results, is dispensed. Consequently, the results generalize several fixed results in metric spaces including the results of G. E. Hardy and T. D. Rogers (1973), R. Kannan (1969), G. Jungck, S. Radenovic, S. Radojevic, and V. Rakocevic (2009), and all the references therein.