TY - JOUR AU - Aghalary, Rasoul AU - Ebadian, Ali AU - Oroujy, Zahra PY - 2012/09/30 Y2 - 2024/03/28 TI - Certain properties of rational functions involving Bessel functions JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 43 IS - 3 SE - Papers DO - 10.5556/j.tkjm.43.2012.814 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/814 SP - 391-398 AB - 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 $H(f)\in M_{n}(\alpha,\beta)$. ER -