On the existence of at least one solution for functional integral equations via the 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.