On Schur Convexity of Some Symmetric Functions
نویسندگان
چکیده
For x x1, x2, . . . , xn ∈ 0, 1 n and r ∈ {1, 2, . . . , n}, the symmetric function Fn x, r is defined as Fn x, r Fn x1, x2, . . . , xn; r ∑ 1≤i1<i2 ···<ir≤n ∏r j 1 1 xij / 1−xij , where i1, i2, . . . , in are positive integers. In this paper, the Schur convexity, Schur multiplicative convexity, and Schur harmonic convexity of Fn x, r are discussed. As consequences, several inequalities are established by use of the theory of majorization.
منابع مشابه
Schur–convexity, Schur Geometric and Schur Harmonic Convexities of Dual Form of a Class Symmetric Functions
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