Turán type inequalities for generalized inverse trigonometric functions

Abstract

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