Schur-Convexity for a Class of Symmetric Functions

Shu-Hong wang^1, and Shu-Ping Bai¹

¹College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

Cite this paper:
Shu-Hong wang and Shu-Ping Bai. Schur-Convexity for a Class of Symmetric Functions. Turkish Journal of Analysis and Number Theory. 2016; 4(1):16-19. doi: 10.12691/tjant-4-1-3

Abstract

In this paper, we discuss Schur convexity for a class of symmetric functions.

Keywords:
Symmetric function Schur- convex function Schur –concave function convex function continuous function majorized

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Y. Chu, G.Wang, X. Zhang, Schur convexity and Hadamard’s inequality, Math. Inequal. Appl., 13 (4) (2010), 725-731.
[2]	I. Franjić, J. Pečarić, Schur-convexity and the Simpson formula, Appl. Math. Lett., (2011).
[3]	N. Elezović, J. Pečarić, A note on Schur-convex functions, Rocky Mountain J. Math., 30 (3) (2000) , 853-856.
[4]	X. Zhang, Y. Chu, Convexity of the integral arithmetic mean of a convex function, Rocky Mountain J. Math. , 40 (3) (2010), 1061-1068.
[5]	A. M. Marshall, I. Olkin, B C. Arnold, Inequalities: Theory of Majorization and its Application (Second Edition). Springer New York, (2011). 101.
[6]	H. N. Shi, J. Zang, Schur convexity, Schur geometric and Schur harmonic convexity of dual form of a class symmetric functions. Journal Mathematical & Inequalities, 8(2) (2014), 349-358.
[7]	H. N. Shi, J. Zang, Schur-convexity of dual form of some symmetric functions, Journal of Inequalities and Applications, 295 (2013), 9 papes.