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Optimal weighted harmonic interpolations between Seiffert means. (English) Zbl 1276.26062

Summary: 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.

MSC:

26E60 Means
26D07 Inequalities involving other types of functions
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