A Hölder-Type Oscillation

★ 8/10Absolute Value Estimation AM-GM inequality

Problem

Let $x, y \in (0, 1)$ . Prove that

\left|x\sin\frac{1}{x^2} - y\sin\frac{1}{y^2}\right| \leqslant 3\sqrt[3]{|x - y|}.

Answer

Solution

Difficulty	8/10
Topics	Absolute Value, Estimation, AM-GM, inequality

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