The inequality of Ky Fan and related results (Q1897274)

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.