## Discrete monotonicity of means and its applications

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**146**(2018), 2091-2102 Request permission

## 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.## References

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## Additional Information

**Ryo Nishimura**- Affiliation: Department of Frontier Materials, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan
- MR Author ID: 1098468
- Email: rrnishimura@gmail.com
- Received by editor(s): March 25, 2017
- Received by editor(s) in revised form: July 10, 2017
- Published electronically: January 8, 2018
- Communicated by: Mourad Ismail
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**146**(2018), 2091-2102 - MSC (2010): Primary 33E05; Secondary 26D15, 33C05
- DOI: https://doi.org/10.1090/proc/13897
- MathSciNet review: 3767360