Abstract and Applied Analysis
Volume 2003 (2003), Issue 6, Pages 353-365

Local solvability of a constrainedgradient system of total variation

C. E. Chidume and H. Zegeye

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 X is a real q-uniformly smooth Banach space and F,K:XX with D(K)=F(X)=X are accretive maps. Under various continuity assumptions on F and K such that 0=u+KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Our method of proof is of independent interest.