The schur convexity of gini mean values in the sense of harmonic mean |
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Authors: | Weifeng Xia |
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Institution: | a School of Teacher Education, Huzhou Teachers College, Huzhou 313000, China b Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China |
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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, a ≥ b,a+b+1 ≥ 0} ∪ {(a,b) : b ≥ a, 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}. |
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Keywords: | Gini mean values Schur convex Schur harmonic convex |
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