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...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of mathematical analysis and applications Jg. 409; H. 1; S. 521 - 529
Hauptverfasser:	Klén, Riku, Vuorinen, Matti, Zhang, Xiaohui
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier Inc 01.01.2014
Schlagworte:	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
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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