Bulletin of the Belgian Mathematical Society - Simon Stevin

Starlikeness of a generalized Bessel function

Rosihan M. Ali, See Keong Lee, and Saiful R. Mondal

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1546570907

Digital Object Identifier
doi:10.36045/bbms/1546570907

Mathematical Reviews number (MathSciNet)
MR3896269

Zentralblatt MATH identifier
07038166

Subjects
Primary: 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$ 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
Bessel function generalized Bessel function starlike function radius of starlikeness

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


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