We study the solvability of functional quadratic integral equations in the space of integrable functions on the interval I = [0, 1]. We concentrate on a.e. monotonic solutions for considered problems. The existence result is obtained under the assumption that the functions involved in the investigated equation satisfy Carathéodory conditions. As a solution space we consider both L 1(I) and L p (I) spaces for p > 1.
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Cichoń et al. (2012) studied this question.