Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 5, Pages 569-581
doi:10.1155/JIA.2005.569

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

Abstract

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.