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The inequality of Ky Fan and related results. (English) Zbl 0834.26013
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.

MSC:
26D15Inequalities for sums, series and integrals of real functions
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References:
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