Alzer, Horst A short proof of Ky Fan’s inequality. (English) Zbl 0759.26014 Arch. Math., Brno 27b, 199-200 (1991). The famous Ky Fan inequality states that if \(A_ n\), \(A_ n'\) denote the arithmetic mean of \(x_ 1,\dots,x_ n\) and \(1-x_ 1,\dots,1-x_ n\), respectively, where \(x_ i\in(0,1/2]\) and \(G_ n\), \(G_ n'\) denote their geometric mean, then we have \(G_ n/G_ n'\leq A_ n/A_ n'\). The author, who obtained some remarkable relations connected to the Ky Fan inequality, in the present paper gives a new proof based on an identity of A. Dinghas [Math. Ann. 178, 315-334 (1968; Zbl 0162.078)]. Reviewer: J.Sándor (Jud.Harghita) Cited in 6 Documents MSC: 26D15 Inequalities for sums, series and integrals Keywords:Ky Fan inequality; arithmetic mean; geometric mean; new proof Citations:Zbl 0162.078 PDFBibTeX XMLCite \textit{H. Alzer}, Arch. Math., Brno 27, 199--200 (1991; Zbl 0759.26014) Full Text: EuDML