Radii of convexity of integral operators
Radii of convexity of integral operators
The object of the present paper is to study of radius of convexity two certain integral operators as follows \begin{equation*} F(z):=\int_{0}^{z}\prod_{i=1}^{n}\left(f'_i(t)\right)^{\gamma_i}{\rm d}t \end{equation*} and \begin{equation*} J(z):=\int_{0}^{z}\prod_{i=1}^{n}\left(f'_i(t)\right)^{\gamma_i}\prod_{j=1}^{m} \left(\frac{g_j(z)}{z}\right)^{\lambda_j}{\rm d}t, \end{equation*} where $\gamma_i, \lambda_i\in\mathbb{C}$, $f_i$ $(1\leq i\leq n)$ and $g_j$ $(1\leq j\leq m)$ belong to the certain subclass of analytic functions.