Sharp bounds for the second Seiffert mean in terms of power means
Classical Analysis and ODEs
2012-06-26 v1
Abstract
For a,b>0 with a\not=b, let T(a,b) denote the second Seiffert mean defined by T(a,b)=((a-b)/(2arctan((a-b)/(a+b)))) and A_{r}(a,b) denote the r-order power mean. We present the sharp bounds for the second Seiffert mean in terms of power means: A_{p_1}(a,b)<T(a,b)\leqA_{p_2}(a,b), where p_1= log_{{\pi}/2}2 and p_2=5/3 can not be improved.
Cite
@article{arxiv.1206.5494,
title = {Sharp bounds for the second Seiffert mean in terms of power means},
author = {Zhen-Hang Yang},
journal= {arXiv preprint arXiv:1206.5494},
year = {2012}
}
Comments
10 pages