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Radii of convexity of integral operators (1804.03868v1)
Published 11 Apr 2018 in math.CV
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){\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.