## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2014 (2014), Article ID 258108, 12 pages.

### Schur $m$-Power Convexity of a Class of Multiplicatively Convex Functions and Applications

Wen Wang and Shiguo Yang

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#### Abstract

We investigate the conditions under which the symmetric functions $$ are Schur $m$-power convex for $x\in {\mathbb{R}}_{++}^{n}$ and $r>0$. As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which generalizes some known results. By applying the theory of majorization, several inequalities involving the $p$th power mean and the arithmetic, the geometric, or the harmonic means are presented.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 258108, 12 pages.

**Dates**

First available in Project Euclid: 2 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1412277005

**Digital Object Identifier**

doi:10.1155/2014/258108

**Mathematical Reviews number (MathSciNet)**

MR3214410

**Zentralblatt MATH identifier**

07022017

#### Citation

Wang, Wen; Yang, Shiguo. Schur $m$ -Power Convexity of a Class of Multiplicatively Convex Functions and Applications. Abstr. Appl. Anal. 2014 (2014), Article ID 258108, 12 pages. doi:10.1155/2014/258108. https://projecteuclid.org/euclid.aaa/1412277005

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