Approximation of solutions of generalized equations of Hammerstein type

Let $H$ be a real Hilbert space. For each $i=1,2,\dots ,m$, let $F_i,K_i:H\to H$ be bounded and monotone mappings. Assume that the generalized Hammerstein equation $u+{\sum }_{i=1}^m{K}_i{F}_{i}u=0$ has a solution in $H$. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation.