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On harmonic representation of means (1310.3063v1)
Published 11 Oct 2013 in math.CA
Abstract: We characterize continuous, symmetric and homogeneous means $M$ that can be represented in the form \begin{equation*} \frac{1}{M(x,y)}=\int_01 \frac{dt}{N\left(\tfrac{x+y}{2}-t\tfrac{x-y}{2},\tfrac{x+y}{2}+t\tfrac{x-y}{2}\right)}. \end{equation*} New inequalities for means are derived from such representation.
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