Existence and local attractivity results for a nonlinear functional integral equation

Abstract In this paper, we prove the existence and local attractivity results for a nonlinear functional integral equation. The equation is considered in the Banach space of real valued functions that are continuous and bounded on $\mathbb{R}_{+}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> </mml:msub> </mml:math> . In our considerations, we apply the measure of noncompactness and the Darbo fixed point theorem. The equation we consider is more general in form and the conditions are less stringent than some existing results.