A double inequality for tanhx

In this paper, we prove that, for x > 0 , 1 − exp ( − x 2 x 2 + 1 ) < tanh x < 1 − exp ( − x 3 x 3 + 1 ) 3 . This solves an open problem proposed by Ivády.

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Bibliographic Details
Published in:Journal of inequalities and applications 2020-01, Vol.2020 (1), p.1-8, Article 19
Main Authors: Zhang, Bo, Chen, Chao-Ping
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Exponential function
Hyperbolic function
Inequality
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Description
Summary:In this paper, we prove that, for x > 0 , 1 − exp ( − x 2 x 2 + 1 ) < tanh x < 1 − exp ( − x 3 x 3 + 1 ) 3 . This solves an open problem proposed by Ivády.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-2289-y