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For x,y > 0 , a,b ∈ R with a + b = 0 , the generalized Muirhead mean is defined by M(a,b;x,y) = x a y b +x b y a 2 1 a+b. In this paper, we prove that M(a,b;x,y) is Schur convex with respect to (x,y) ∈ (0,∞)×(0,∞) if and only if (a,b) ∈ {(a,b) ∈ R 2 : (a−b) 2 a+b > 0 & ab 0} and Schur concave with respect to (x,y) ∈ (0,∞)×(0,∞) if and only if (a,b) ∈ {(a,b)(More)
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