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Inequalities for symmetric means

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Abstract

A study is made of a symmetric form of the m-th degree and the class of symmetric means (arithmetic) associated with it, the simplest of these being the Muirhead means. A number of new theorems on comparability, related to Muirhead's Theorem, are proven.

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Literature cited

  1. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, London (1934).

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  2. John Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, New York (1958).

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  3. R. E. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Proc. Edinburgh Math. Soc.,21, 144–157 (1903).

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch of the Academy of Sciences of the USSR, USSR

    G. A. Bekishev

Authors
  1. G. A. Bekishev
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Additional information

Translated from Matematicheskie Zametki, Vol 3, No. 2, pp. 133–144, February, 1968.

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Bekishev, G.A. Inequalities for symmetric means. Mathematical Notes of the Academy of Sciences of the USSR 3, 83–91 (1968). https://doi.org/10.1007/BF01094326

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  • DOI: https://doi.org/10.1007/BF01094326

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