A linear operator associated with a certain variation of the Bessel function Jν(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_\nu (z)$$\end{document} and related conformal mappings

In this paper we introduce an operator associated with a certain variation of the Bessel function Jν(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_\nu (z)$$\end{document} in the unit disk. By using this operator and the method of differential subordination we obtain some properties such as convolution and radius of starlikeness of the function class Ωp(k,c,λ;h)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _p(k,c,\lambda ;h)$$\end{document}.