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In this paper, using properties of the Henstock-Kurzweil integrad and corresponding theorems, we prove existence theorems for the equation x' = f(t,xt) and inclusion x' € F(t,xt) in a Banach space where / is Henstock-Kurzweil integrable and satisfies some additional conditions.

RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL INTEGRALS