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