Approximation of solutions of Hammerstein equations with bounded strongly accretive nonlinear operators

Suppose XX is a real qq-uniformly smooth Banach space and F,K:X→XF,K:X→X are bounded strongly accretive maps with D(K)=F(X)=XD(K)=F(X)=X. Let u∗u∗ denote the unique solution of the Hammerstein equation u+KFu=0u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗u∗. No invertibility assumption is imposed on KK and the operators KK and FF need not be defined on compact subsets of XX. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included.