Schur convexity properties for a class of symmetric functions with applications
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Authors
Wei-Mao Qian
- School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China.
Yu-Ming Chu
- Department of Mathematics, Huzhou University, Huzhou 313000, China.
Abstract
In the article, we prove that the symmetric function
\[
F_{n}\left(x_{1}, x_{2}, \cdots, x_{n}; r\right)=\sum_{1\leq i_{1}<i_{2}<\cdots<i_{r}\leq n}\prod_{j=1}^{r}\left(\frac{1+x_{i_{j}}}{1-x_{i_{j}}}\right)^{1/r}
\]
is Schur convex, Schur multiplicatively convex and Schur harmonic convex on \([0, 1)^{n}\), and establish several new analytic
inequalities by use of the theory of majorization, where \(r\in \{1, 2, \cdots, n\}\) and \(i_{1}, i_{2}, \cdots i_{n}\) are integers.
Share and Cite
ISRP Style
Wei-Mao Qian, Yu-Ming Chu, Schur convexity properties for a class of symmetric functions with applications, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 841--849
AMA Style
Qian Wei-Mao, Chu Yu-Ming, Schur convexity properties for a class of symmetric functions with applications. J. Nonlinear Sci. Appl. (2018); 11(6):841--849
Chicago/Turabian Style
Qian, Wei-Mao, Chu, Yu-Ming. "Schur convexity properties for a class of symmetric functions with applications." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 841--849
Keywords
- Schur convex
- Schur multiplicatively convex
- Schur harmonic convex
- symmetric function
MSC
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