Local solvability of a constrainedgradient system of total variation

摘要

SupposeXis a realq-uniformly smooth Banach space andF,K:X→XwithD(K)=F(X)=Xare accretive maps. Under various continuity assumptions onFandKsuch that0=u+KFuhas a solution, iterative methods which converge strongly tosuch a solution are constructed. No invertibility assumption isimposed onKand the operatorsKandFneed not be defined on compact subsets ofX. Our method of proof is of independent interest.