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Abstract and Applied Analysis
Volume 2003 (2003), Issue 6, Pages 353-365
http://dx.doi.org/10.1155/S1085337503209052

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 Hindawi Publishing Corporation. 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.

Abstract

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.