# An application of the Picard operator technique to functional integral equations

## Abstract

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.

## Authors

V.A. Ilea
(Babes Bolyai Univ.)

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

## Keywords

Functional-integral equation; weakly Picard operators; data dependence

## Cite this paper as:

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

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##### Journal

Journal of Nonlinear and Convex Analysis

Yokohama, Japan

1345-4773

1880-5221

MR3649198