On Seiffert-like means
arXiv:1309.1244 · doi:10.7153/jmi-09-83
Abstract
We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1-μ)min(x,y)+ μmax(x,y)<= M(x,y)<= (1-ν)min(x,y)+ νmax(x,y) and M((x+y)/2-μ(x-y)/2,(x+y)/2+μ(x-y)/2)<= N(x,y)<= M((x+y)/2-ν(x-y)/2,(x+y)/2+ν(x-y)/2) for some known means.