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A best-possible double inequality between Seiffert and harmonic means. (English) Zbl 1273.26038

Summary: In this paper, we establish a new double inequality between the Seiffert and harmonic means. { } The achieved results are inspired by the papers of J. Sándor [Arch. Math. 76, No.1, 34–40 (2001; Zbl 0976.26015)] and P. A. Hästö [Math. Inequal. Appl. 7, No. 1, 47–53 (2004; Zbl 1049.26006)], and the methods from M.-K. Wang et al. [J. Math. Inequal. 4, No. 4, 581–586 (2010; Zbl 1204.26053)]. The inequalities we obtain improve the existing corresponding results and, in some sense, are optimal.

MSC:

26E60 Means
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[1] doi:10.1007/s000130050539 · Zbl 0976.26015 · doi:10.1007/s000130050539
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