Parameter convexity and concavity of generalized trigonometric functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Karp, D. B.^1,2  Prilepkina, E. G.^1,2 

[1] Far Eastern Fed Univ, Vladivostok 690950, Russia

[2] FEBRAS, Inst Appl Math, Vladivostok 690041, Russia

关键词: Generalized trigonometric functions;    Generalized hyperbolic functions;    Eigenfunctions of p-Laplacian;    Log-convexity;    Log-concavity;    Turan type inequality;   

DOI  :  10.1016/j.jmaa.2014.07.017

来源: Elsevier

【 摘 要 】

We study the convexity properties of the generalized trigonometric functions viewed as functions of the parameter. We show that p -> sin(p)(y) and p -> cos(p)(y) are log-concave on the appropriate intervals while p -> tan(p)(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 (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free