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arXiv · 1504.07431

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

Bappaditya Bhowmik
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Abstract

In this article we consider a family $\mathcal{C}(A, B)$ of analytic and locally univalent functions on the open unit disc $\ID=\{z :|z|<1\}$ 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 $z_0 \in \ID$ and $f"(0)$ whenever $f$ varies over the class $\mathcal{C}(A, B)$.

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Bappaditya Bhowmik. 2015-04-28. Regions of variability for a class of analytic and locally univalent functions defined by subordination. https://arxiv.org/abs/1504.07431

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