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  • Research Article
  • Open Access

Schur-convexity of the complete elementary symmetric function

Journal of Inequalities and Applications20062006:67624

  • Received: 2 October 2004
  • Accepted: 27 January 2005
  • Published:


We prove that the complete elementary symmetric function and the function are Schur-convex functions in , where are nonnegative integers, , . For which, some inequalities are established by use of the theory of majorization. A problem given by K. V. Menon (Duke Mathematical Journal 35 (1968), 37–45) is also solved.


  • Nonnegative Integer
  • Symmetric Function
  • Mathematical Journal
  • Elementary Symmetric Function
  • Duke Mathematical Journal


Authors’ Affiliations

Department of Mathematics and Physics, Nanhua University, Hengyang, Hunan, 421001, China


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© Kaizhong Guan 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.