Abstract and Applied Analysis
Volume 2003 (2003), Issue 6, Pages 353-365
Local solvability of a constrainedgradient system of total variation
The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste 34100, Italy
Received 27 October 2001
Copyright © 2003 C. E. Chidume and H. Zegeye. 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.
Suppose is a real -uniformly smooth Banach space and with are accretive maps. Under various continuity assumptions on and such that has a solution, iterative methods which converge strongly to
such a solution are constructed. No invertibility assumption is
imposed on and the operators and need not be defined on compact subsets of . Our method of proof is of independent interest.