Skip to main content

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

  • 397 Accesses


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].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

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.

Download citation

  • DOI:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-2228-5

  • Online ISBN: 978-94-017-2226-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics