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Zbl 0834.26013
Alzer, Horst
The inequality of Ky Fan and related results.
(English)
[J] Acta Appl. Math. 38, No.3, 305-354 (1995). ISSN 0167-8019; ISSN 1572-9036/e

This survey paper presents refinements, extensions, and variants of the well-known Ky Fan inequality $$\prod^n_{i = 1} \bigl( y_i/(1 - y_i) \bigr)^{1/n} < \sum^n_{i = 1} y_i \left/ \sum^n_{i = 1} \right. (1 - y_i),$$ valid for all real numbers $y_i \in (0,1/2]$ $(i = 1, \ldots, n)$ which are not all equal. In the list of 54 references, there are 24 of the author of this paper.
[J.E.Pečarić (Zagreb)]
MSC 2000:
*26D15 Inequalities for sums, series and integrals of real functions

Keywords: arithmetic mean; geometric mean; Ky Fan inequality

Cited in: Zbl 0991.26013 Zbl 0872.26007

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