Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 105, Issue 1, Pages 412-421Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2011.08.004
Keywords
Hamy symmetric function; Second dual form; Schur concave; Schur multiplicatively convex; Schur harmonic convex
Categories
Funding
- NSF of China [11071069]
- NSF of Zhejiang Province [Y6100170, Y7080185]
- Innovation Team Foundation of the Department of Education of Zhejiang Province [T200924]
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For x = (x(1), x(2), ... , x(n)) is an element of R-+(n), the second dual form of the Hamy symmetric function is defined by H-n** (x, r) = H-n** (x(1), x(2), ... , x(n); r) = Pi(1 <= i1<...<= n) (Sigma(r)(j=1) x(ij))(1/r), where r is an element of {1, 2, ... , n} and i(1), i(2), ... , i(n) are positive integers. In this paper, we prove that H-n* (x, r) is Schur concave, and Schur multiplicatively and harmonic convex in R-+(n). Some applications in inequalities and reliability theory are presented. (C) 2011 Elsevier Inc. All rights reserved.
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