Bounds for Quotients of Inverse Trigonometric and Inverse Hyperbolic Functions

We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin−1xsinh−1x and tanh−1xtan−1x. The main results provide polynomial bounds using even quadratic functions and exponential bounds under the form eax2. Graph validation is also performed...

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Bibliographic Details
Published in:Axioms 2022-05, Vol.11 (6), p.262
Main Authors: Thool, Sumedh B., Bagul, Yogesh J., Dhaigude, Ramkrishna M., Chesneau, Christophe
Format: Article
Language:English
Subjects:
exponential function
Functions, Exponential
Functions, Inverse
Hyperbolic functions
Inequality
inverse hyperbolic functions
inverse trigonometric functions
Mathematical analysis
Mathematical functions
Mathematical research
Polynomials
Quadratic equations
Quotients
Trigonometrical functions
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Summary:We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin−1xsinh−1x and tanh−1xtan−1x. The main results provide polynomial bounds using even quadratic functions and exponential bounds under the form eax2. Graph validation is also performed.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11060262