## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Starlikeness of a generalized Bessel function

#### Abstract

This paper investigates three functions $\mathtt{f}_{a, \nu}$, $\mathtt{g}_{a, \nu}$ and $\mathtt{h}_{a, \nu}$ in the class $\mathcal{A}$ consisting of analytic functions $f$ in the unit disk satisfying $f(0)=f'(0)-1=0$. Here $a \in \{1, 2, 3, \ldots\},$ and $\nu$ is real. Each function is related to the generalized Bessel function. The radius of starlikeness of positive order is obtained for each of the three functions. Further, the best range on $\nu$ is determined for a fixed $a$ to ensure the functions $\mathtt{f}_{a, \nu}$ and $\mathtt{g}_{a, \nu}$ are starlike of positive order in the entire unit disk. When $a=1,$ the results obtained reduced to earlier known results.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 4 (2018), 527-540.

Dates
First available in Project Euclid: 4 January 2019

https://projecteuclid.org/euclid.bbms/1546570907

Digital Object Identifier
doi:10.36045/bbms/1546570907

Mathematical Reviews number (MathSciNet)
MR3896269

Zentralblatt MATH identifier
07038166

#### Citation

Ali, Rosihan M.; Lee, See Keong; Mondal, Saiful R. Starlikeness of a generalized Bessel function. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 4, 527--540. doi:10.36045/bbms/1546570907. https://projecteuclid.org/euclid.bbms/1546570907