Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean - Hongya Gao; Jianling Guo; Wanguo Yu (Abstract and Applied Analysis)
For 1<r<+∞, we find the least value α and the greatest value β such that the inequality Hα(a,b)<Ar(a,b)<Hβ(a,b) holds for all a,b>0 with a≠b. Here, Hω(a,b) and Ar(a,b) are the generalized Heronian and the power means of two positive numbers a and b, respectively.