Fixed Point Theory and Applications
Volume 2005 (2005), Issue 1, Pages 11-33

Regularization of nonlinear Ill-posed equations with accretive operators

Ya. I. Alber,1 C. E. Chidume,2 and H. Zegeye2

1Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
2Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, Trieste 340314, Italy

Received 11 October 2004

Copyright © 2005 Ya. I. 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 the regularization methods for solving equations with arbitrary accretive operators. We establish the strong convergence of these methods and their stability with respect to perturbations of operators and constraint sets in Banach spaces. Our research is motivated by the fact that the fixed point problems with nonexpansive mappings are namely reduced to such equations. Other important examples of applications are evolution equations and co-variational inequalities in Banach spaces.