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A New Dual Hardy-Hilbert's Inequality with some Parameters and its Reverse

Zhong, Wuyi

  • Received : 2008.04.06
  • Accepted : 2008.12.11
  • Published : 2009.09.30

Abstract

By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.

Keywords

Euler-Maclaurin summation formula;dual Hardy-Hilbert's inequality;reverse form;best constant factor;equivalent form

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