Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 431754 | https://doi.org/10.1155/S1085337503209052

C. E. Chidume, H. Zegeye, "Local solvability of a constrainedgradient system of total variation", Abstract and Applied Analysis, vol. 2003, Article ID 431754, 13 pages, 2003. https://doi.org/10.1155/S1085337503209052

Local solvability of a constrainedgradient system of total variation

Received27 Oct 2001


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.

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.

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