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Sharp generalized Seiffert mean bounds for the Toader mean of order 4

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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 the article, we present the best possible parameters \(\alpha ,\beta \) such that the double inequality

$$\begin{aligned} S_{\alpha }(a,b)<T_{4}(a,b)<S_{\beta }(a,b) \end{aligned}$$

holds for \(a, b>0\) with \(a\ne b\), and provide new bounds for the complete elliptic integral of the second kind, where \(S_{p}(a,b)\) and \(T_{4}(a,b)\) are the generalized Seiffert mean and Toader mean of order 4, respectively.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 11971142), the Natural Science Foundation of Zhejiang Province (Grant No. LY19A010012) and HZNU Scientific Research Funding (Grant No. 4085C50218204112).

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

    Yanlin Li & Tiehong Zhao

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  1. Yanlin Li
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  2. Tiehong Zhao
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Li, Y., Zhao, T. Sharp generalized Seiffert mean bounds for the Toader mean of order 4. RACSAM 115, 106 (2021). https://doi.org/10.1007/s13398-021-01048-w

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