Some properties of a class of symmetric functions

The Schur-convexity and Schur-geometric-convexity of a class of symmetric functions are investigated. As consequences some new proofs of the well-known Ky Fan's inequality and Shapiro's inequality are presented, respectively. We also give another proof of a problem posted by S. Gabler in [...

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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 336; H. 1; S. 70 - 80
1. Verfasser: Guan, Kaizhong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: San Diego, CA Elsevier Inc 01.12.2007
Elsevier
Schlagworte:
Algebraic combinatorics
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Ky Fan's inequality
Mathematical analysis
Mathematics
Schur-convex function
Schur-geometrically-convex function
Sciences and techniques of general use
Several complex variables and analytic spaces
Shapiro's inequality
Shapiro's inequality
Schur-convex function
Schur-geometrically-convex function
Ky Fan's inequality
Mathematical analysis
Geometric convexity
Convex function
Application
ISSN:0022-247X, 1096-0813
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:The Schur-convexity and Schur-geometric-convexity of a class of symmetric functions are investigated. As consequences some new proofs of the well-known Ky Fan's inequality and Shapiro's inequality are presented, respectively. We also give another proof of a problem posted by S. Gabler in [S. Gabler, Aufgabe 830, Elem. Math. 3 (1980) 124–125]. Some interesting matrix and geometric inequalities are established to show the applications of our results.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.02.064