Strong Convergence Theorems for Solutions of Equations of Hammerstein Type

Abstract

We consider an auxiliary operator, defined in a real Hilbert space in terms of and , that is, monotone and Lipschitz mappings (resp., monotone and bounded mappings). We use an explicit iterative process that converges strongly to a solution of equation of Hammerstein type. Furthermore, our results improve related results in the literature.

Algorithm for equations of Hammerstein type and applications

“…It is known that (J E +t 0 F ) and (J E * +t 0 K) are bijections (see e.g, Chuang [17]). It can be easily verified that if E is a smooth, strictly convex and reflexive Banach space and F : E → E * is a monotone mapping with R(J E + tF ) = E * , then for each t > 0, the resolvent J E t of F defined by…”

Existence Solution of Volterra Hammerstein Equation in L^p Space

“…Mustafa Nader gave conditions that ensure the existence and the uniqueness of the solution for equation (1) in the space [4]. Authors in [5][6][7][8] found sequences converged to the exact solution of equation 1under such assumptions.…”