A Sharp Double Inequality between Harmonic and Identric Means - Yu-Ming Chu; Miao-Kun Wang; Zi-Kui Wang (Abstract and Applied Analysis)
We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa+(1-p)b,pb+(1-p)a)<I(a,b)<H(qa+(1-q)b,qb+(1-q)a) holds for all a,b>0 with a≠b. Here, H(a,b), and I(a,b) denote the harmonic and identric means of two positive numbers a and b, respectively.