Abstract and Applied Analysis
Volume 2003 (2003), Issue 4, Pages 193-216

Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces

Yakov Alber,1 Simeon Reich,1 and Jen-Chih Yao2

1Department of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, Israel
2Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804 , Taiwan

Received 21 January 2002

Copyright © 2003 Yakov Alber 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.


We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stability of these methods with respect to perturbations of the operators and the constraint sets.