On Erdélyi–Kober Quadratic Functional-Integral Equation in Banach Algebra

Abstract

Using the technique of a suitable measure of noncompactness in Banach algebra, we prove an existence theorem for some functional-integral equations in Banach algebra, namely Erdélyi–Kober quadratic functional-integral equation. This equation contains as particular cases a lot of integral equations that appear in many branches of nonlinear analysis and its applications. The obtained result is illustrated by an example.