Approximating solutions of Hammerstein type equations in Banach spaces

Abstract

Let X be a real Banach space and X^? be its dual. Let F: X → X^? and K: X^? → X be Lipschitz monotone mappings. In this paper an explicit iterative scheme is constructed for approximating solutions of the Hammerstein type equation, 0 = u + KF u, when they exist. Strong convergence of the scheme is obtained under appropriate conditions. Our results improve and unify many of the results in the literature.