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Sharp power mean bounds for the lemniscate type means

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we present sharp power mean bounds for the so-called lemniscate type means, which were introduced by Neuman (Math Pannon 18(1):77–94, 2007). The obtained results measure what the distance is between the lemniscate-type means and power means. As applications, several new bounds for the arc lemniscate functions are established.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11971142) and the Natural Science Foundation of Zhejiang Province (Grant Nos. LY19A010012, LQY18G030001).

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Authors and Affiliations

  1. School of Mathematics, Hangzhou Normal University, Hangzhou, 311121, China

    Tie-Hong Zhao & Zhong-Hua Shen

  2. Department of Mathematics, Huzhou University, Huzhou, 313000, China

    Yu-Ming Chu

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  1. Tie-Hong Zhao
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  2. Zhong-Hua Shen
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  3. Yu-Ming Chu
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All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

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Correspondence to Yu-Ming Chu.

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Zhao, TH., Shen, ZH. & Chu, YM. Sharp power mean bounds for the lemniscate type means. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 115, 175 (2021). https://doi.org/10.1007/s13398-021-01117-0

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  • DOI: https://doi.org/10.1007/s13398-021-01117-0

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