Parameter convexity and concavity of generalized trigonometric functions

2014/02/14 by Dmitrii Karp, D. B. Karp, Karp, D. B. +2
Mathematics · #33B99 #33E30 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #math.CA #msc:33B99 #msc:33E30

paper · pdf · doi:10.48550/arxiv.1402.3357

15 pages, no figures

arxiv created 2014/02/14 · openalex publication_date 2014/02/14 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the convexity properties of the generalized trigonometric functions considered as functions of 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 the major part of a conjecture put forward in a recent paper by Baricz, Bhayo and Vuorinen.

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