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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Veröffentlicht in:	Axioms 2022-05, Vol.11 (6), p.262
Hauptverfasser:	Thool, Sumedh B., Bagul, Yogesh J., Dhaigude, Ramkrishna M., Chesneau, Christophe
Format:	Artikel
Sprache:	eng
Schlagworte:	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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Beschreibung
Zusammenfassung:	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