On logarithm of circular and hyperbolic functions and bounds for exp(±x<sup>2</sup>)-Reference-Cited by-同舟云学术

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

Published:2022-11-01 Issue:1 Volume:14 Page:160-165
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Sándor József¹

Affiliation:

1. Babeş-Bolyai University , Department of Mathematics Kogălniceanu street Nr. 1 , Cluj-Napoca , Romania

Abstract

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

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/ausm-2022-0011

Reference10 articles.

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

2. [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

3. [3] D. S. Mitrinovic, Analytic inequalities, Springer, 1970.10.1007/978-3-642-99970-3

4. [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

5. [5] E. Neuman, J. Sándor, Optimal inequalities for hyperbolic and trigonometric functions, Bull. Math. Anal. Appl., 3 (2011), 177–181.

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