Solvability of Functional Integral Equations in the Fréchet Space $${C(\Omega)}$$ C ( Ω )

Abstract

This work deals with the existence of solutions for a class of nonlinear functional integral equations of Volterra type in the Frechet space of continuous functions on an unbounded subset \({\Omega}\) of \({\mathbb{R}^n}\). The equation was considered by Arab et al. (J Math 13(3):1197–1210, 2015). By choosing a different functional space and a different fixed point theorem in conjunction with some measures of noncompactness, we show that existence of continuous solutions can be proved under weaker conditions.