A numerical approach for solving hammerstein integral equations in banach spaces

Mostefa Nadir
Department of Mathematics University of Msila.

\(^{1}\)Corresponding Author: mostefanadir@yahoo.fr

Copyright © 2014 Mostefa Nadir. 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.

Published: December, 2014.

Abstract

In this work, we give a weaker conditions guarantee the boundedness of the Hammerstein integral equation in \(L^p\) spaces, also we study conditions of the convergence of the approximate solution to the exact one of the integral equation using the successive approximations method. Finally, we treat numerical examples compared with other papers in order to confirm the efficiency of our results.

Keywords:

Hammerstein integral equation, successive approximation, interpolation spaces.