Certain properties of rational functions involving Bessel functions

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Published: Sep 30, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.814
Keywords:
Rational functions-Starlike function-Bessel functions-Convolution

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Rasoul Aghalary
Ali Ebadian
Zahra Oroujy

Abstract

Let $g_{\upsilon}(z)$ be the classical Bessel function of the first kind of order $\upsilon$ and $f$ be an analytic function defined on the unit disc $\Delta$. Suppose the operator $H(f)$ be defined by $H(f)(z)=\frac{z}{\frac{z}{f(z)}*\frac{g_{\upsilon}(z)}{z}}$. In this paper we identify subfamily $M_{n}(\alpha,\beta)$ of univalent functions and obtain conditions on the parameter $\upsilon$ such that $f\in M_{n}(\alpha,\beta)$ implies $H(f)\in M_{n}(\alpha,\beta)$.

Article Details

How to Cite
Aghalary, R., Ebadian, A., & Oroujy, Z. (2012). Certain properties of rational functions involving Bessel functions. Tamkang Journal of Mathematics, 43(3), 391–398. https://doi.org/10.5556/j.tkjm.43.2012.814
Issue
Vol. 43 No. 3 (2012)
Section
Papers
Author Biographies

Rasoul Aghalary

Department of Mathematics, Urmia Uniersity, Urmia

PH.D , Reader

Ali Ebadian

Department of Mathematics, Urmia University,Urmia, Iran

P.h.D Reader

Zahra Oroujy

Dept of Maths, Urmia University, Urmia, Iran

P.h.D Student

 

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