## Banach Journal of Mathematical Analysis

### On the existence of at least a solution for functional integral equations via measure of noncompactness

#### Abstract

In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation

$$u(t)=g(t,u(t))+\int_{0}^{t}G(t,s,u(s))\,ds,\quad t\in{[0,+\infty[},$$ in the space of all bounded and continuous real functions on $\mathbb{R}_{+}$, under suitable assumptions on $g$ and $G$. Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.

#### Article information

Source
Banach J. Math. Anal., Volume 11, Number 3 (2017), 497-512.

Dates
Accepted: 28 July 2016
First available in Project Euclid: 19 April 2017

https://projecteuclid.org/euclid.bjma/1492618126

Digital Object Identifier
doi:10.1215/17358787-2017-0003

Mathematical Reviews number (MathSciNet)
MR3679893

Zentralblatt MATH identifier
06754300

#### Citation

Vetro, Calogero; Vetro, Francesca. On the existence of at least a solution for functional integral equations via measure of noncompactness. Banach J. Math. Anal. 11 (2017), no. 3, 497--512. doi:10.1215/17358787-2017-0003. https://projecteuclid.org/euclid.bjma/1492618126

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