Parameter convexity and concavity of generalized trigonometric functions

We study the convexity properties of the generalized trigonometric functions viewed as functions of the parameter. We show that p→sinp⁡(y) and p→cosp⁡(y) are log-concave on the appropriate intervals while p→tanp⁡(y) is log-convex. We also prove similar facts about the generalized hyperbolic function...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Journal of mathematical analysis and applications Ročník 421; číslo 1; s. 370 - 382
Hlavní autoři:	Karp, D.B., Prilepkina, E.G.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.01.2015
Témata:	Eigenfunctions of p-Laplacian Generalized hyperbolic functions Generalized trigonometric functions Log-concavity Log-convexity Turán type inequality Log-concavity Generalized trigonometric functions Generalized hyperbolic functions Eigenfunctions of p-Laplacian Turán type inequality Log-convexity
ISSN:	0022-247X, 1096-0813
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	We study the convexity properties of the generalized trigonometric functions viewed as functions of the parameter. We show that p→sinp⁡(y) and p→cosp⁡(y) are log-concave on the appropriate intervals while p→tanp⁡(y) is log-convex. We also prove similar facts about the generalized hyperbolic functions. In particular, our results settle a major part of the conjecture recently put forward in [4].
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2014.07.017