Second order differential-functional inequalities for bounded functions (Q1417873)

Let \(F\) denote a real Fréchet space of all functions \(u\in C^\infty(\mathbb{R},\mathbb{R})\) such that all derivatives \(u^{(n)}\), \(n\geq 1\), are bounded. \(F\) is endowed with the classical system of seminorms and ordered by the classical cone of nonnegative functions. The main result proved in the paper creates some version of the Nagumo-Westphal lemma for differential-functional inequalities in \(F\).