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Inequalities for Ratios of Integrals

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General Inequalities 4

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Abstract

A unified method is presented for finding bound estimates on ratios of consecutive-moments of a non-negative function having a continuous first or second derivative of one sign. One extension of this work leads to a converse of the Cauchy-Schwarz-Buniakowski inequality and to a best possible constant.

Other results are found that strengthen and generalize some integral inequality of Ting and of Sendov and Skordev concerning moments of concave non-negative functions.

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References

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Author information

Authors and Affiliations

  1. Applied Mathematics Department, La Trobe University, Victoria, 3083, Australia

    Dieter K. Ross

Authors
  1. Dieter K. Ross
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Editor information

Editors and Affiliations

  1. Mathematisches Institut I, Universität Karlsruhe, Kaiserstrasse 12, D-7500, Karlsruhe 1, Germany

    Wolfgang Walter

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© 1984 Springer Basel AG

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Ross, D.K. (1984). Inequalities for Ratios of Integrals. In: Walter, W. (eds) General Inequalities 4. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6259-2_12

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  • DOI: https://doi.org/10.1007/978-3-0348-6259-2_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6261-5

  • Online ISBN: 978-3-0348-6259-2

  • eBook Packages: Springer Book Archive

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