CrossRef Open Access 2022

New Bounds for Arithmetic Mean by the Seiffert-like Means

Ling Zhu

Abstrak

By using the power series of the functions 1/sinnt and cost/sinnt (n=1,2,3,4,5), and the estimation of the ratio of two adjacent Bernoulli numbers, we obtained new bounds for arithmetic mean A by the weighted arithmetic means of Mtan1/3Msin2/3 and 13Mtan+23Msin,Mtanh1/3Msinh2/3 and 13Mtanh+23Msinh, where Mtan(x,y) and Msin(x,y), Mtanh(x,y) and Msinh(x,y) are the tangent mean, sine mean, hyperbolic tangent mean and hyperbolic sine mean, respectively. The upper and lower bounds obtained in this paper are compared in detail with the conclusions of the previous literature.

Penulis (1)

Ling Zhu

Format Sitasi

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Zhu, L. (2022). New Bounds for Arithmetic Mean by the Seiffert-like Means. https://doi.org/10.3390/math10111789

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: CrossRef
DOI: 10.3390/math10111789
Akses: Open Access ✓