Schur convexity properties for a class of symmetric functions with applications

Volume 11, Issue 6, pp 841--849 http://dx.doi.org/10.22436/jnsa.011.06.10
Publication Date: May 03, 2018 Submission Date: January 24, 2016 Revision Date: March 27, 2018 Accteptance Date: March 28, 2018

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.


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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


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