Discrete monotonicity of means and its applications

Nishimura, Ryo

doi:10.1090/proc/13897

Discrete monotonicity of means and its applications
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by Ryo Nishimura

Proc. Amer. Math. Soc. 146 (2018), 2091-2102

DOI: https://doi.org/10.1090/proc/13897

Published electronically: January 8, 2018

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Abstract:

In this paper, we obtain new inequalities for the logarithmic mean and the complete elliptic integral of the first kind. In order to prove the inequalities, we use the monotonicity property of sequences defined by these functions. Additionally, we apply our approach to previous studies. As a result, we get refinements of known inequalities.

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