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
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.