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Sharp power mean bounds for Seiffert mean

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Abstract

In this paper, we find the greatest value p = log2/(log π − log 2) = 1.53 … and the least value q = 5/3 = 1.66 … such that the double inequality M p (a, b) < T(a, b) < M q (a, b) holds for all a, b > 0 with a ≠ b. Here, M p (a, b) and T (a, b) are the p-th power and Seiffert means of two positive numbers a and b, respectively.

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Authors and Affiliations

  1. School of Mathematics and Computation Science, Hunan City University, Yiyang, 413000, China

    Yong-min Li, Miao-kun Wang & Yu-ming Chu

Authors
  1. Yong-min Li
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  2. Miao-kun Wang
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  3. Yu-ming Chu
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Corresponding author

Correspondence to Yu-ming Chu.

Additional information

Supported by the National Natural Science Foundation of China (61174076, 61374086, 11171307) and the Natural Science Foundation of Zhejiang Province (LY13A010004).

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Li, Ym., Wang, Mk. & Chu, Ym. Sharp power mean bounds for Seiffert mean. Appl. Math. J. Chin. Univ. 29, 101–107 (2014). https://doi.org/10.1007/s11766-014-3008-6

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  • DOI: https://doi.org/10.1007/s11766-014-3008-6

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