Geometric Properties of Functions Containing Derivatives of Bessel Functions

Abstract

In this paper our aim is to find the radii of $\gamma$-Spirallike of order $\alpha$ and convex $\gamma$-Spirallike of order $\alpha$ for three different kinds of normalizations of the function $N_\nu(z)=az^2J_\nu^{\prime\prime}(z)+bzJ_\nu^{\prime}(z)+cJ_\nu(z),$ where $J_\nu(z)$ is the Bessel function of the first kind of order $\nu.$ Moreover, the $\mathcal{S}^*\left(\varphi\right)-$radii and $\mathcal{C}\left(\varphi\right)-$radii of these normalized functions are investigated. The tables are created and visual verification with graphs are made by giving special values to the real numbers $a,$ $b$ and $c$ in the obtained results.