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Discrete monotonicity of means and its applications


Author: Ryo Nishimura
Journal: Proc. Amer. Math. Soc. 146 (2018), 2091-2102
MSC (2010): Primary 33E05; Secondary 26D15, 33C05
DOI: https://doi.org/10.1090/proc/13897
Published electronically: January 8, 2018
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Ryo Nishimura
Affiliation: Department of Frontier Materials, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan
Email: rrnishimura@gmail.com

DOI: https://doi.org/10.1090/proc/13897
Keywords: Complete elliptic integrals, inequalities, infinite product
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
Article copyright: © Copyright 2018 American Mathematical Society

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