Inequalities for the generalized trigonometric and hyperbolic functions

The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional p-Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinović–Adamović’s inequality...

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Vydáno v:	Journal of mathematical analysis and applications Ročník 409; číslo 1; s. 521 - 529
Hlavní autoři:	Klén, Riku, Vuorinen, Matti, Zhang, Xiaohui
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.01.2014
Témata:	Cusa–Huygens-type inequalities Generalized hyperbolic functions Generalized trigonometric functions Huygens-type inequalities Mitrinović–Adamović’s inequality Lazarević’s inequality Wilker-type inequalities Generalized trigonometric functions Huygens-type inequalities Generalized hyperbolic functions Wilker-type inequalities Cusa–Huygens-type inequalities Mitrinović–Adamović’s inequality Lazarević’s inequality
ISSN:	0022-247X, 1096-0813
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Popis
Shrnutí:	The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional p-Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinović–Adamović’s inequality, Lazarević’s inequality, Huygens-type inequalities, Wilker-type inequalities, and Cusa–Huygens-type inequalities, are generalized to the case of generalized functions.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2013.07.021