Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 847170, 19 pages
Research Article

Common Fixed Point Theorems for a Finite Family of Discontinuous and Noncommutative Maps

Department of Mathematics, National Changhua University of Education, Changhua 50058, Taiwan

Received 30 December 2010; Accepted 20 February 2011

Academic Editor: Jong Kim

Copyright © 2011 Lai-Jiu Lin and Sung-Yu Wang. 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.


We study common fixed point theorems for a finite family of discontinuous and noncommutative single-valued functions defined in complete metric spaces. We also study a common fixed point theorem for two multivalued self-mappings and a stationary point theorem in complete metric spaces. Throughout this paper, we establish common fixed point theorems without commuting and continuity assumptions. In contrast, commuting or continuity assumptions are often assumed in common fixed point theorems. We also give examples to show our results. Results in this paper except those that generalized Banach contraction principle and those improve and generalize recent results in fixed point theorem are original and different from any existence result in the literature. The results in this paper will have some applications in nonlinear analysis and fixed point theory.