The Schur-harmonic-convexity of dual form of the Hamy symmetric function

Authors

  • Junxia Meng College of Mathematics and Information Science, Jiaxing University, Jiaxing 314001, P. R. China Author
  • Yuming Chu Department of Mathematics, Huzhou Teachers College, Huzhou 313000, P. R. China Author
  • Xiaomin Tang Department of Mathematics, Huzhou Teachers College, Huzhou 313000, P. R. China Author

Keywords:

Dual form, Hamy symmetric function, Schur convex, Schur harmonic convex

Subjects:

26B25, 05E05, 26D20

Abstract

We prove that the dual form of the Hamy symmetric function $$ H_n(x, r)=H_n(x_1, x_2, \dots, x_n; r)=\prod_{1\leq i_1<\cdots<i_r\leq n}\biggl(\sum_{j=1}^{r}x_{i_j}^{\frac{1}{r}}\biggr) $$ is Schur harmonic convex in $\R_+^n$. As applications, some inequalities are established by use of the theory of majorization.

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Published

2010-01-15

Issue

Vol. 62 No. 1 (2010): Vol. 62, Issue 1

Section

Articles

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Copyright (c) 2010 Authors retain copyright to their work.

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This work is licensed under a Creative Commons Attribution 4.0 International License.