Radii of convexity of integral operators

Abstract

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)^{γ_i}{\rm d}t \end{equation*} and \begin{equation*} J(z):=\int_{0}^{z}\prod_{i=1}^{n}\left(f'_i(t)\right)^{γ_i}\prod_{j=1}^{m} \left(\frac{g_j(z)}{z}\right)^{λ_j}{\rm d}t, \end{equation*} where ${\gamma }_i,{\lambda }_i\in \mathbb{C}$, $f_i$ $(1\le i\le n)$ and $g_j$ $(1\le j\le m)$ belong to the certain subclass of analytic functions.

7 pages