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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.