Some properties of a generalized Hamy symmetric function and its applications

This paper is concerned with the generalized Hamy symmetric function∑n(x,r;f)=∑1⩽i1<i2<⋯<ir⩽nf(∏j=1rxij1r), where f is a positive function defined in a subinterval of (0,+∞). Some properties, including Schur-convexity, geometric Schur-convexity and harmonic Schur-convexity are investigated....

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 376; no. 2; pp. 494 - 505
Main Authors: Guan, Kaizhong, Guan, Ruke
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.04.2011
Elsevier
Subjects:
Algebraic combinatorics
Combinatorics
Combinatorics. Ordered structures
Convexity
Exact sciences and technology
Functional analysis
Functions of a complex variable
Hamy symmetric function
Inequality
Mathematical analysis
Mathematics
Monotonicity
Schur-convexity
Sciences and techniques of general use
Several complex variables and analytic spaces
Schur-convexity
Convexity
Hamy symmetric function
Monotonicity
Inequality
Mathematical analysis
Geometric convexity
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:This paper is concerned with the generalized Hamy symmetric function∑n(x,r;f)=∑1⩽i1<i2<⋯<ir⩽nf(∏j=1rxij1r), where f is a positive function defined in a subinterval of (0,+∞). Some properties, including Schur-convexity, geometric Schur-convexity and harmonic Schur-convexity are investigated. As applications, several inequalities are obtained, some of which extend the known ones.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.10.014