Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 569-581

Existence and approximate solutions of nonlinear integral equations

Abderrazek Karoui

Département de Mathématiques, Faculté des Sciences de Bizerte, Université 7 Novembre à Carthage, Jarzouna 7021, Tunisia

Received 10 October 2003; Revised 4 December 2003

Copyright © 2005 Abderrazek Karoui. 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.


We investigate the existence of continuous solutions on compact intervals of some nonlinear integral equations. The existence of such solutions is based on some well-known fixed point theorems in Banach spaces such as Schaefer fixed point theorem, Schauder fixed point theorem, and Leray-Schauder principle. A special interest is devoted to the study of nonlinear Volterra equations and to the numerical treatment of these equations.