Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON HARDY AND PÓLYA-KNOPP'S INEQUALITIES

  • Kwon, Ern Gun (Department of Mathematics Education Andong National University) ;
  • Jo, Min Ju (Department of Mathematics Graduate School, Andong National University)
  • Received : 2018.01.08
  • Accepted : 2018.03.13
  • Published : 2018.05.15
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Abstract

Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

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References

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