Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 963802, 15 pages
http://dx.doi.org/10.5402/2012/963802
Research Article

Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type with Lipschitz and Bounded Nonlinear Operators

Section de Mathématiques Appliquées, Université Gaston Berger, BP 234 Saint Louis, Senegal

Received 20 March 2012; Accepted 10 May 2012

Academic Editors: M. Idemen and J. Kou

Copyright © 2012 N. Djitte and M. Sene. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm and F, K : 𝐸 β†’ 𝐸 be Lipschitz accretive maps with 𝐷 ( 𝐾 ) = 𝑅 ( 𝐹 ) = 𝐸 . Suppose that the Hammerstein equation 𝑒 + 𝐾 𝐹 𝑒 = 0 has a solution. An explicit iteration method is shown to converge strongly to a solution of the equation. No invertibility assumption is imposed on K and the operator F is not restricted to be angle-bounded. Our theorems are significant improvements on important recent results (e.g., (Chiume and Djitte, 2012)).