International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 4, Pages 251-257
Fixed point theorems for nonexpansive mappings
on nonconvex sets in UCED Banach spaces
1Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan
2Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan
3Department of Mathematics and Science Education, National Hsinchu Teacher's College, Hsinchu 300, Taiwan
Received 25 July 2001; Revised 10 January 2002
Copyright © 2002 Wei-Shih Du 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.
It is shown that every asymptotically regular or -firmly
nonexpansive mapping has a fixed point
whenever is a finite union of nonempty weakly compact convex
subsets of a Banach space which is uniformly convex in every
direction. Furthermore, if is any compatible family of strongly nonexpansive self-mappings on such a and the graphs of , , have a nonempty intersection, then , , have a common fixed point in .