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On logarithm of circular and hyperbolic functions and bounds for exp(±x2) Cover

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On logarithm of circular and hyperbolic functions and bounds for exp(±x2)

Acta Universitatis Sapientiae, Mathematica

Volume 14 (2022): Issue 1 (November 2022)

By: József Sándor

Open Access

|Nov 2022

We show that certain known or new inequalities for the logarithm of circular hyperbolic functions imply bounds for exp(±x²) proved in [1].

[1] Y. J. Bagul, C. Chesneau, Some sharp circular and hyperbolic bounds of exp(±x²) with applications. Appl. Anal. Discrete Math., 14 (2020), 239–254.10.2298/AADM190123010B
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[2] B. A. Bhayo, J. Sándor, On certain old and new trigonometric and hyperbolic inequalities. Analysis Mathematica, 41 (2015), No. 1–2, 3–15.10.1007/s10476-015-0102-9
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[3] D. S. Mitrinovic, Analytic inequalities, Springer, 1970.10.1007/978-3-642-99970-3
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[4] E. Neuman, J. Sándor, On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker and Huygens inequalities, Math. Ineq. Appl., 13 (2010), 715–723.10.7153/mia-13-50
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[5] E. Neuman, J. Sándor, Optimal inequalities for hyperbolic and trigonometric functions, Bull. Math. Anal. Appl., 3 (2011), 177–181.
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[6] J. Sándor, Two sharp inequalities for trigonometric and hyperbolic functions, Math. Ineq. Appl., 15 (2012), 409–413.10.7153/mia-15-35
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[7] J. Sándor, On Huygens’ inequalities and the theory of means, Intern. J. Math. Math. Sci., volume 2012, Article ID597490, 1–9.10.1155/2012/597490
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[8] J. Sándor, Sharp Cusa-Huygens and related inequalities, Notes on Number Theory and Discrete Mathematics, 19 (2013), No. 1, 50–54.
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[9] E. Neuman, J. Sándor, Inequalities for hyperbolic functions, Appl. Math. Comp., 218 (2012), Issue 18, 9291–9295.10.1016/j.amc.2012.03.007
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[10] J. Sándor, Theory of means and their inequalities, www.math.ubbcluj.ro/~jsandor/lapok/Sandor-Jozsef-Theory of means and their inequalities.pdf (2018).
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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2022-0011 | Journal eISSN: 2066-7752

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Language: English

Page range: 160 - 165

Submitted on: Oct 11, 2021

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Published online: Nov 18, 2022

Published in print: Nov 1, 2022

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

integral inequalities

MSC:

Related subjects:

General mathematics

© 2022 József Sándor, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 14 (2022): Issue 1 (November 2022)

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