An application of the Picard operator technique to functional integral equations

In this paper we consider a functional integral equation of the form
\[
x(t)=g(t,x(t),x(h(t)))+\int_{a}^{t} f(s,x(h(s)))ds+\int_{a}^{b} K(s,x(h(s)))ds, \ \ t \in [a,b].
\]

Using the weakly Picard operator technique we establish existence, data dependence and comparison results for the solutions of the above equation.

V.A. Ilea
(Babes Bolyai Univ.)

D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,
Technical University of Cluj-Napoca)

V.A. Ilea, D. Otrocol, An application of the Picard operator technique to functional integral equations, J. Nonlinear Convex Anal., Vol. 18 (2017) no. 3, pp. 405-413

http://www.ybook.co.jp/online2/jncav18-3.html