Note on the Hölder norm estimate of the function $x\sin(1/x)$

preprint2014arXivOpen access

In this paper, we prove the following inequality: for any $x, y>0$ , there holds $\big|x\sin\frac{1}{x} - y\sin\frac{1}{y} \big| \leq \sqrt{2|x - y|}.$

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Note on the Hölder norm estimate of the function $x\sin(1/x)$

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Note on the Hölder norm estimate of the function xsin⁡(1/x)x\sin(1/x)xsin(1/x)

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Note on the Hölder norm estimate of the function $x\sin(1/x)$