Turán type inequalities for generalized inverse trigonometric functions

Árpád Baricz, Barkat Ali Bhayo, Matti Vuorinen

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we study the inverse of the eigenfunction sinpof 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.

Original languageEnglish
Pages (from-to)303-313
Number of pages11
JournalFilomat
Volume29
Issue number2
DOIs
Publication statusPublished - Jan 1 2015

    Fingerprint

Keywords

  • Bernstein functions
  • Completely monotone functions
  • Eigenfunctions of p-Laplacian
  • Generalized trigonometric function
  • Log-concavity
  • Log-convexity
  • Turán-type inequalities

ASJC Scopus subject areas

  • Mathematics(all)

Cite this