On Ky Fan-type inequalities. Aequationes Mathematicae, 62(3):310-320, 2001. abstract bibtex Let An, Gn, Hn (respectively, A′n, G′n, H′n) denote the unweighted arithmetic, geometric, harmonic means of x1, . . . , xn (respectively, 1 - xn, . . . , 1 xj), where xj ∈ (0,1/2] (j = 1, . . . , n). In 1984, Wang and Wang established (Gn/G′n)n ≤ (An/A′n)n-1 Hn/H′n, which refines the well-known Ky Fan inequality Gn/G′n ≤ An/A′n. The validity of the converse inequality (Hn/H′n)n-1 An/A′n ≤ (Gn/G′n)n (0.1) was conjectured in 1988. In this paper we give a proof for (0.1). © Birkhäuser Verlag, 2001.
@article{17844383559,
abstract = "Let An, Gn, Hn (respectively, A′n, G′n, H′n) denote the unweighted arithmetic, geometric, harmonic means of x1, . . . , xn (respectively, 1 - xn, . . . , 1 xj), where xj ∈ (0,1/2] (j = 1, . . . , n). In 1984, Wang and Wang established (Gn/G′n)n ≤ (An/A′n)n-1 Hn/H′n, which refines the well-known Ky Fan inequality Gn/G′n ≤ An/A′n. The validity of the converse inequality (Hn/H′n)n-1 An/A′n ≤ (Gn/G′n)n (0.1) was conjectured in 1988. In this paper we give a proof for (0.1). © Birkhäuser Verlag, 2001.",
number = "3",
year = "2001",
title = "On Ky Fan-type inequalities",
volume = "62",
pages = "310-320",
journal = "Aequationes Mathematicae"
}
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