Turán type inequalities for generalized inverse trigonometric functions

Abstract

In this paper we study the inverse of the eigenfunction ${\sin }_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Turán type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Turán type inequality for a series considered by Ramanujan, involving the digamma function.

arXiv comment10 pages

References in corpus (5)

• Generalized Convexity and Inequalities
• Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian
• Log-convexity and log-concavity of hypergeometric-like functions
• Geometric convexity of the generalized sine and the generalized hyperbolic sine
• Inequalities for generalized trigonometric and hyperbolic sine functions

Cited by in corpus (4)

• On generalized complete $(p,q)$-elliptic integrals
• Parameter convexity and concavity of generalized trigonometric functions
• A look at generalized trigonometric functions as functions of their two parameters and further new properties
• Convexity properties of generalized trigonometric and hyperbolic functions