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arXiv · 1210.6749

Inequalities for the generalized trigonometric and hyperbolic functions

Riku Klén·Matti Vuorinen·Xiaohui Zhang
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Abstract

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 inequality, Lazarević's inequality, Huygens-type inequalities, Wilker-type inequalities, and Cuza-Huygens-type inequalities, are generalized to the case of generalized functions.

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Riku Klén, Matti Vuorinen, Xiaohui Zhang. 2012-10-25. Inequalities for the generalized trigonometric and hyperbolic functions. https://arxiv.org/abs/1210.6749

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