Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 870980, 18 pages
doi:10.1155/2010/870980
Research Article

On Fixed Point Theorems for Multivalued Contractions

Zeqing Liu,1 Wei Sun,1 Shin Min Kang,2 and Jeong Sheok Ume3

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Applied Mathematics, Changwon National University, Changwon 641-773, Republic of Korea

Received 13 August 2010; Accepted 15 November 2010

Academic Editor: N. J. Huang

Copyright © 2010 Zeqing Liu et al. 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

Three concepts of multivalued contractions in complete metric spaces are introduced, and the conditions guaranteeing the existence of fixed points for the multivalued contractions are established. The results obtained in this paper extend genuinely a few fixed point theorems due to Ćirić (2009) Feng and Liu (2006) and Klim and Wardowski (2007). Five examples are given to explain our results.