Sharp Power Mean Bounds for Sándor Mean - Yu-Ming Chu; Zhen-Hang Yang; Li-Min Wu (Abstract and Applied Analysis)
We prove that the double inequality Mp(a,b)<X(a,b)<Mq(a,b) holds for all a,b>0 with a≠b if and only if p≤1/3 and q≥log 2/(1+log 2)=0.4093…, where X(a,b) and Mr(a,b) are the Sándor and rth power means of a and b, respectively.