Geometric properties of certain integral operators involving Hornich operations

S. Kumar

Published 2021-06-11Version 1

In this article, we investigate some standard geometric properties of the integral operator $$ C_{\alpha,\beta}[f,g](z)=\int_{0}^{z}\bigg(\frac{f(w)}{w}\bigg)^\alpha (g'(w))^\beta dw, \,\,\, \alpha,\beta \in \mathbb{R} \text{ and } |z|<1, $$ where $f$ and $g$ are elements of certain classical families of normalized analytic functions defined on the unit disk. Here, the exponents are chosen in such a way that the respective functions are analytic in suitable branches.