Regions of variability for a class of analytic and locally univalent functions defined by subordination

摘要

In this article, we consider a family $mathcal{C}(A,B)$ of analytic and locally univalent functions on the open unit disc $mathbb{D} = {z : |z| 1}$ in the complex plane that properly contains the well-known Janowski class of convex univalent functions. In this article, we determine the exact set of variability of log$(f'(z_0))$ with fixed $z_0 in mathbb{D}$ and $f''(0)$ whenever e?‘“ varies over the class $mathcal{C}(A,B)$.