Fixed Point Theory and Applications
Volume 2005 (2005), Issue 2, Pages 125-135
doi:10.1155/FPTA.2005.125
Iterative schemes with some control conditions for a family of
finite nonexpansive mappings in Banach spaces
1Department of Mathematics, College of Natural Sciences, Dong-A University, Busan 604-714, Korea
2Department of Mathematics Education, College of Education, and the Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Korea
3Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
Received 19 September 2004; Revised 8 January 2005
Copyright © 2005 Jong Soo Jung 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
The iterative schemes with some control conditions for a family of finite nonexpansive mappings are established in a Banach space. The main theorem improves results of Jung and Kim (also Bauschke). Our results also improve the corresponding results of Cho et al., Shioji and Takahashi, Xu, and Zhou et al. in certain Banach spaces and of Lions, O'Hara et al., and Wittmann in a framework of a Hilbert space, respectively.