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 + KFu; 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.

Mathematics Subject Classification (2010): 47H30, 47H05, 34A34.

Keywords: Hammerstein type equation, monotone mapping, nonlinear equations