On Seiffert-like means
Abstract
We investigate the representation of homogeneous, symmetric means in the form M(x,y)=x-y2f((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)+ μ max(x,y)<= M(x,y)<= (1-)min(x,y)+ max(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-(x-y)/2,(x+y)/2+(x-y)/2) for some known means.
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