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, Lazarević’s inequality, Huygens-type inequalities, Wilker-type inequalities, and Cusa–Huygens-type inequalities, are generalized to the case of generalized functions.