Abstract and Applied Analysis 
Volume 2003 (2003), Issue 4, Pages 193-216
doi:10.1155/S1085337503203018

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

Abstract

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.