Local solvability of a constrainedgradient system of total variation
C.E. Chidume, Habtu Zegeye · Abstract and Applied Analysis · 2003
Suppose X is a real q‐uniformly smooth Banach space and F, K : X → X 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.