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The optimal generalized logarithmic mean bounds for Seiffert’s mean. (English) Zbl 1274.26084

Summary: For \(p\in \mathbb{R}\), the generalized logarithmic mean \(L_p (a, b)\) and Seiffert’s mean \(T (a, b)\) of two positive real numbers \(a\) and \(b\) are defined, respectively. In this paper, we find the greatest \(p\) and the least \(q\) such that the double-inequality \(L_p (a, b) <T(a, b)< L_q (a, b)\) holds for all \(a, b > 0\) and \(a\neq b\).

MSC:

26E60 Means
26D20 Other analytical inequalities
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