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We prove some existence theorems for nonlinear integral equations of the Urysohn type x(t) = φ(t) + λ a 0 f(t, s, x(s)) ds and Volterra type x(t) = φ(t) + t 0 f(t, s, x(s)) ds, t ∈ Ia = [0, a], where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock–Kurzweil integral.

On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals