Abstract and Applied Analysis

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 F n , k ( x , r ) = 1 i 1 < i 2 < < i k n   f ( j = 1 k x i j r ) 1 / r ,   k = 1,2 , , n, are Schur m -power convex for x 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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