Approximation of solutions of nonlinear equations of Hammerstein type in Hilbert space
C.E. Chidume, Habtu Zegeye · Proceedings of the American Mathematical Society · 2004
Let $H$ be a real Hilbert space. Let $F:D(F)\subseteq H\rightarrow H$, $K:D(K)\subseteq H\to H$ be bounded monotone mappings with $R(F)\subseteq D(K)$, where $D(F)$ and $D(K)$ are closed convex subsets of $H$ satisfying certain conditions. Suppose the equation $0=u+KFu$ has a solution in $D(F)$. Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on $K$, and the operators $K$ and $F$ need not be defined on compact subsets of $H$.