Inequalities for the generalized trigonometric and hyperbolic functions
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- 作者：Riku Kl¨¦n ; Matti Vuorinen ; Xiaohui Zhang
- 关键词：Generalized trigonometric functions ; Generalized hyperbolic functions ; Mitrinovi?&ndash ; Adamovi?&rsquo ; s inequality Lazarevi?&rsquo ; s inequality ; Huygens-type inequalities ; Wilker-type inequalities ; Cusa&ndash ; Huygens-type inequalities
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2014
- 出版时间：1 January, 2014
- 年：2014
- 卷：409
- 期：1
- 页码：521-529
- 全文大小：391 K
文摘
The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional -Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinovi?-Adamovi?¡¯s inequality, Lazarevi?¡¯s inequality, Huygens-type inequalities, Wilker-type inequalities, and Cusa-Huygens-type inequalities, are generalized to the case of generalized functions.