Strong convergence theorem for integral equations of Hammerstein type in Hilbert spaces

摘要

Let H be a real Hilbert space. Let F:H→H be a bounded, coercive and maximal monotone mapping. Let K:H→H be a bounded and maximal monotone mapping. Let K and F satisfy the range condition. Suppose that u∗∈H is a solution to Hammerstein equation u+KFu=0. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation. Our iterative scheme in this paper seems far simpler than the iterative scheme used by Chidume and Ofoedu (2011) [13] and their strong assumption is dispensed with. We give some examples of our result so that it will find serious applications and be of much interest to our readers.