Turán type inequalities for generalized inverse trigonometric functions

A. Baricz, Barkat Ali Bhayo, Matti Vuorinen

Research output: Contribution to journalArticle

3 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 - 2015

Fingerprint

Inverse trigonometric function
Generalized Inverse
Inverse hyperbolic function
Digamma Function
P-Laplace Operator
Ramanujan
Eigenfunctions
Deduce
Series

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

Turán type inequalities for generalized inverse trigonometric functions. / Baricz, A.; Bhayo, Barkat Ali; Vuorinen, Matti.

In: Filomat, Vol. 29, No. 2, 2015, p. 303-313.

Research output: Contribution to journalArticle

Baricz, A. ; Bhayo, Barkat Ali ; Vuorinen, Matti. / Turán type inequalities for generalized inverse trigonometric functions. In: Filomat. 2015 ; Vol. 29, No. 2. pp. 303-313.
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