Convexity properties of generalized trigonometric and hyperbolic functions. (English) Zbl 1394.33006
Summary: We study the power mean inequality for generalized trigonometric and hyperbolic functions with two parameters. The generalized \(p\)-trigonometric and \((p,q)\)-trigonometric functions were introduced by P. Lindqvist [Ric. Mat. 44, No. 2, 269–290 (1995; Zbl 0944.33002)] and S. Takeuchi [J. Math. Anal. Appl. 385, No. 1, 24–35 (2012; Zbl 1232.34029)], respectively.
MSC:
| 33E20 | Other functions defined by series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26E60 | Means |
Keywords:
power mean; eigenfunctions of \(p\)-Laplacian; generalized trigonometric functions; generalized inverse trigonometric functions; convexity with respect to power means; geometrical convexityReferences:
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