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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 187348, 5 pages
http://dx.doi.org/10.1155/2013/187348
Research Article

Fixed Point Theorems of Quasicontractions on Cone Metric Spaces with Banach Algebras

1School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
2Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China

Received 5 August 2013; Accepted 23 October 2013

Academic Editor: Simeon Reich

Copyright © 2013 Hao Liu and Shaoyuan Xu. 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 introduce the concept of quasicontractions on cone metric spaces with Banach algebras, and by a new method of proof, we will prove the existence and uniqueness of fixed points of such mappings. The main result generalizes the well-known theorem of Ćirić (Ćirić 1974).