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

Iterative approximation of solutions of nonlinear equations of Hammerstein type

Abstract

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.