Schur convexity properties for a class of symmetric functions with applications

Qian, Wei-Mao ¹ ; Chu, Yu-Ming ²

¹ School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China
² Department of Mathematics, Huzhou University, Huzhou 313000, China

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 841-849.

Résumé

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}$

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.

Détail

DOI : 10.22436/jnsa.011.06.10

Classification : 05E05, 26B25
Keywords: Schur convex, Schur multiplicatively convex, Schur harmonic convex, symmetric function

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