The radius of convexity of normalized Bessel functions of the first kind

A. Baricz, Róbert Szász

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

In this paper, we determine the radius of convexity for three kinds of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are starlike-univalent and convex-univalent, respectively, on the determined disks. The key tools in the proofs of the main results are some new Mittag-Leffler expansions for quotients of Bessel functions of the first kind, special properties of the zeros of Bessel functions of the first kind and their derivative, and the fact that the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function of the first kind. Moreover, we find the optimal parameters for which these normalized Bessel functions are convex in the open unit disk. In addition, we disprove a conjecture of Baricz and Ponnusamy concerning the convexity of the Bessel function of the first kind.

Original languageEnglish
JournalAnalysis and Applications
Issue number2
DOIs
Publication statusAccepted/In press - 2014

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Bessel function of the first kind
Bessel functions
Convexity
Radius
Bessel Functions
Zero
Disprove
Optimal Parameter
Unit Disk
Quotient
Derivative
Derivatives

Keywords

  • convex functions
  • Dini function
  • minimum principle for harmonic functions
  • Normalized Bessel functions of the first kind
  • radius of convexity
  • residue theorem
  • zeros of Bessel functions

ASJC Scopus subject areas

  • Applied Mathematics
  • Analysis

Cite this

The radius of convexity of normalized Bessel functions of the first kind. / Baricz, A.; Szász, Róbert.

In: Analysis and Applications, No. 2, 2014.

Research output: Contribution to journalArticle

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