Inequalities for the generalized trigonometric and hyperbolic functions (1210.6749v1)

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 Mitrinovi\'c-Adamovi\'c inequality, Lazarevi\'c's inequality, Huygens-type inequalities, Wilker-type inequalities, and Cuza-Huygens-type inequalities, are generalized to the case of generalized functions.