Convexity properties of generalized trigonometric and hyperbolic functions

DOI10.1007/s00010-013-0222-xzbMath1394.33006arXiv1301.0699OpenAlexW2154739051WikidataQ110233601 ScholiaQ110233601MaRDI QIDQ2350251

Árpád Baricz, Riku Klén, Barkat Ali Bhayo

Publication date: 19 June 2015

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0699

zbMATH Keywords

power meangeneralized trigonometric functionseigenfunctions of \(p\)-Laplaciangeometrical convexitygeneralized inverse trigonometric functionsconvexity with respect to power means

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20) Convexity of real functions in one variable, generalizations (26A51) Means (26E60)

Related Items (13)

The inverse hyperbolic tangent function and Jacobian sine function ⋮ Inequalities and bounds for the \(p\)-generalized trigonometric functions ⋮ Sharp exponential type inequalities for the arc lemniscate sine function with applications ⋮ A necessary and sufficient condition for the convexity of the generalized elliptic integral of the first kind with respect to Hölder mean ⋮ Generalized Gudermannian function ⋮ Inequalities for the generalized trigonometric and hyperbolic functions ⋮ On certain new means generated by generalized trigonometric functions ⋮ On a function involving generalized complete \((p, q)\)-elliptic integrals ⋮ Monotonicity and inequalities related to the generalized inverse lemniscate functions ⋮ Functional inequalities for generalized complete elliptic integrals with two parameters ⋮ A survey for generalized trigonometric and hyperbolic functions ⋮ A necessary and sufficient condition for the convexity of the one-parameter generalized inverse trigonometric sine function according to power mean ⋮ Logarithmic mean inequality for generalized trigonometric and hyperbolic functions

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