Iterative approximation of solutions of nonlinear equations of Hammerstein type

Abstract

Suppose $X$ is a real $q$-uniformly smooth Banach space and $F,K:X\to X$ with $D\left(K\right)=F\left(X\right)=X$ 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.