Articles

THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN

  • XIA Wei-Feng ,
  • CHU Yu-Ming
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  • School of Teacher Education, Huzhou Teachers College, Huzhou 313000, China; Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received date: 2008-11-10

  Revised date: 2009-11-25

  Online published: 2011-05-20

Supported by

Supported by the  NSFC (11071069), the NSF of Zhejiang Province (D7080080 and Y7080185), and the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924).

Abstract

We prove that the Gini mean values S(a, b; x, y) are Schur harmonic convex with respect to (x, y)∈ (0, ∞)×(0,∞) if and only if (a, b)∈{(a,b):a≥0, ab,a+b+1≥0}∪{(a, b):b≥0, ba, a+b+1≥0} and Schur harmonic concave with respect to (x, y)∈(0, ∞)×(0, ∞) if and only if (a, b)∈{(a, b):a≤0, b≤0, a+b+1≤0}.

Cite this article

XIA Wei-Feng , CHU Yu-Ming . THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 1103 -1112 . DOI: 10.1016/S0252-9602(11)60301-9

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