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arXiv · 1309.1244

On Seiffert-like means

Alfred Witkowski
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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.

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Alfred Witkowski. 2013-09-05. On Seiffert-like means. https://doi.org/10.7153/jmi-09-83

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