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

Junxia Meng; Yuming Chu; Xiaomin Tang

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 $H_{n} (x, r) = H_{n} (x_{1}, x_{2}, \dots, x_{n}; r) = \prod_{1 \leq i_{1} < \dots < i_{r} \leq n} (\sum_{j = 1}^{r} x_{i_{j}}^{\frac{1}{r}})$ is Schur harmonic convex in $\R_{+}^{n}$ . As applications, some inequalities are established by use of the theory of majorization.

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

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