Bounds for radii of starlikeness and convexity of some special functions

Ibrahim Aktaş, A. Baricz, Halit Orhan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler-Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre-Pólya class of real entire functions plays an important role in our study.

Original languageEnglish
Pages (from-to)211-226
Number of pages16
JournalTurkish Journal of Mathematics
Volume42
Issue number1
DOIs
Publication statusPublished - Jan 1 2018

Fingerprint

Starlikeness
Special Functions
Convexity
Radius
Friedrich Wilhelm Bessel
Upper and Lower Bounds
Zero
Entire Function
Rayleigh
Normalization
Euler
Derivative

Keywords

  • And Bessel functions
  • And Bessel functions
  • And convex functions
  • And convexity
  • Laguerre-Pólya class of entire functions
  • Lommel
  • Mittag-Leffler expansions
  • Radius of univalence
  • Starlike
  • Starlikeness
  • Struve
  • Struve
  • Univalent
  • Zeros of Lommel

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bounds for radii of starlikeness and convexity of some special functions. / Aktaş, Ibrahim; Baricz, A.; Orhan, Halit.

In: Turkish Journal of Mathematics, Vol. 42, No. 1, 01.01.2018, p. 211-226.

Research output: Contribution to journalArticle

Aktaş, Ibrahim ; Baricz, A. ; Orhan, Halit. / Bounds for radii of starlikeness and convexity of some special functions. In: Turkish Journal of Mathematics. 2018 ; Vol. 42, No. 1. pp. 211-226.
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