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Part of the book series: Mathematics and Its Applications ((MAIA,volume 31))

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Abstract

In this chapter we consider the means associated with various types of symmetric functions and their generalisations. This is a completely different kind of generalisation of the arithmetic and geometric means to those considered in chapters three and four. Symmetric functions arose naturally in the study of algebraic equations; see for instance Uspensky [2, Chap. IX]. As a result many of the results have been known for a long time — the basic inequality 2.1(1) below being due to Newton [1] and Campbell [1].

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© 1988 Springer Science+Business Media Dordrecht

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Bullen, P.S., Mitrinović, D.S., Vasić, P.M. (1988). Symmetric Means. In: Means and Their Inequalities. Mathematics and Its Applications (East European Series) , vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2226-1_5

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  • DOI: https://doi.org/10.1007/978-94-017-2226-1_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-2228-5

  • Online ISBN: 978-94-017-2226-1

  • eBook Packages: Springer Book Archive

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