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The schur convexity of gini mean values in the sense of harmonic mean
Authors:Weifeng Xia
Institution:a School of Teacher Education, Huzhou Teachers College, Huzhou 313000, China
b Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
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):a0,ab,a+b+10}{(a,b):ba,a+b+10} and Schur harmonic concave with respect to (x,y)(0,∞)×(0,∞) if and only if (a,b){(a,b):a0,b0,a+b+10}.
Keywords:Gini mean values  Schur convex  Schur harmonic convex
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