Inequalities for the generalized trigonometric and hyperbolic functions
arXiv:1210.6749
Abstract
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 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.
12 pages