Convexity properties of generalized trigonometric and hyperbolic functions

Abstract

We study the power mean inequality of the generalized trigonometric and hyperbolic functions with two parameters. The generalized $p$-trigonometric and $(p,q)$-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi, respectively.

9 pages, 1 figure

References in corpus (5)

• Geometric convexity of the generalized sine and the generalized hyperbolic sine
• Turán type inequalities for generalized inverse trigonometric functions
• Power mean inequality of generalized trigonometric functions
• Inequalities for generalized trigonometric and hyperbolic sine functions
• On generalized trigonometric functions with two parameters