Optimal weighted harmonic interpolations between Seiffert means
Volume 130 / 2013
Colloquium Mathematicum 130 (2013), 265-279
MSC: Primary 26E60; Secondary 26D07.
DOI: 10.4064/cm130-2-8
Abstract
We provide a set of optimal estimates of the form $$ \frac {1-\mu }{\mathcal {A}(x,y)}+ \frac {\mu }{\mathcal {M}(x,y)}\leq \frac {1}{\mathcal {B}(x,y)}\leq \frac {1-\nu }{\mathcal {A}(x,y)}+ \frac {\nu }{\mathcal {M}(x,y)} $$ where $\mathcal {A}<\mathcal {B}$ are two of the Seiffert means $L,P,M,T$, while $\mathcal {M}$ is another mean greater than the two.
