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Schur-convexity of the complete elementary symmetric function

Journal of Inequalities and Applications volume 2006, Article number: 67624 (2006) Cite this article

Abstract

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.

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Authors and Affiliations

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

    Kaizhong Guan

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  1. Kaizhong Guan
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Correspondence to Kaizhong Guan.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Guan, K. Schur-convexity of the complete elementary symmetric function. J Inequal Appl 2006, 67624 (2006). https://doi.org/10.1155/JIA/2006/67624

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  • DOI: https://doi.org/10.1155/JIA/2006/67624

Keywords

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