Remarks on some systems of two simultaneous functional inequalities

Abstract. We study the real (measurable and continuous at a point) functions that satisfy, almost everywhere, some systems of two simultaneous functional inequalities. In particular, we obtain generalizations and extensions of some earlier results of D. Krassowska, J. Matkowski,
P. Montel, and T. Popoviciu.

Key words and phrases. Functional inequality, microperiodic function, Lebesgue measurability, Baire property, \(\sigma\)-ideal.