Strong convergence theorem for approximation of solutions of equations of Hammerstein type

Let HH be a real Hilbert space. Let K,F:H→HK,F:H→H be bounded, continuous and monotone mappings. Suppose that u∗∈Hu∗∈H is a solution to the Hammerstein equation u+KFu=0u+KFu=0. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation. Furthermore, we give some examples to show that our result is interdisciplinary in nature, covers a large variety of areas and should be of much interest to a wide audience.