### Abstract

In this paper, our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for Wright function and properties of real zeros of the Wright function and its derivative. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized Wright functions. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind. Some open problems are also proposed, which may be of interest for further research.

Original language | English |
---|---|

Pages (from-to) | 97-117 |

Number of pages | 21 |

Journal | Mathematical Communications |

Volume | 23 |

Issue number | 1 |

Publication status | Published - May 1 2018 |

### Fingerprint

### Keywords

- Laguerre-pólya class of entire functions
- Mittag-leffler expansion
- Radius of starlikeness and convexity
- Starlike functions
- Univalent
- Wright function
- Zeros of wright function

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Applied Mathematics

### Cite this

*Mathematical Communications*,

*23*(1), 97-117.

**Radii of starlikeness and convexity of wright functions.** / Baricz, A.; Toklu, Evrim; Kadıoğlu, E.

Research output: Contribution to journal › Article

*Mathematical Communications*, vol. 23, no. 1, pp. 97-117.

}

TY - JOUR

T1 - Radii of starlikeness and convexity of wright functions

AU - Baricz, A.

AU - Toklu, Evrim

AU - Kadıoğlu, E.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - In this paper, our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for Wright function and properties of real zeros of the Wright function and its derivative. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized Wright functions. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind. Some open problems are also proposed, which may be of interest for further research.

AB - In this paper, our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for Wright function and properties of real zeros of the Wright function and its derivative. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized Wright functions. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind. Some open problems are also proposed, which may be of interest for further research.

KW - Laguerre-pólya class of entire functions

KW - Mittag-leffler expansion

KW - Radius of starlikeness and convexity

KW - Starlike functions

KW - Univalent

KW - Wright function

KW - Zeros of wright function

UR - http://www.scopus.com/inward/record.url?scp=85054626857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054626857&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85054626857

VL - 23

SP - 97

EP - 117

JO - Mathematical Communications

JF - Mathematical Communications

SN - 1331-0623

IS - 1

ER -