Table of Contents
ISRN Mathematical Analysis
Volume 2012, Article ID 169751, 12 pages
Research Article

Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type

1Mathematics Institute, African University of Sciences and Technology, Abuja, Nigeria
2Mathematics Department, Gaston Berger University, Saint Louis, Senegal

Received 29 November 2011; Accepted 10 January 2012

Academic Editors: F. Arandiga and J. Cui

Copyright © 2012 C. E. Chidume and N. Djitté. 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.


Suppose that 𝐻 is a real Hilbert space and 𝐹,πΎβˆΆπ»β†’π» are bounded monotone maps with 𝐷(𝐾)=𝐷(𝐹)=𝐻. Let π‘’βˆ— denote a solution of the Hammerstein equation 𝑒+𝐾𝐹𝑒=0. An explicit iteration process is shown to converge strongly to π‘’βˆ—. No invertibility or continuity assumption is imposed on 𝐾 and the operator 𝐹 is not restricted to be angle-bounded. Our result is a significant improvement on the Galerkin method of BrΓ©zis and Browder.