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Schur-convexity of the complete elementary symmetric function

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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Correspondence to Kaizhong Guan.

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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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Keywords

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