Approximation of solutions of generalized equations of Hammerstein type

Let HH be a real Hilbert space. For each i=1,2,…,mi=1,2,…,m, let Fi,Ki:H→HFi,Ki:H→H be bounded and monotone mappings. Assume that the generalized Hammerstein equation u+∑i=1mKiFiu=0 has a solution in HH. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation.