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
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.
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.