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Note on the H\"{o}lder norm estimate of the function $x\sin(1/x)$

Classical Analysis and ODEs 2014-07-28 v1

Abstract

In this paper, we prove the following inequality: for any x,y>0x, y>0, there holds xsin1xysin1y2xy.\big|x\sin\frac{1}{x} - y\sin\frac{1}{y} \big| \leq \sqrt{2|x - y|}.

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Cite

@article{arxiv.1407.6871,
  title  = {Note on the H\"{o}lder norm estimate of the function $x\sin(1/x)$},
  author = {Jiaqiang Mei and Haifeng Xu},
  journal= {arXiv preprint arXiv:1407.6871},
  year   = {2014}
}

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15 pages