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arXiv · 2407.14922

Geometric subfamily of functions convex in some direction and Blaschke products

Liulan Li·Saminthan Ponnusamy
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Abstract

Consider the family of locally univalent analytic functions $h$ in the unit disk $|z|<1$ with the normalization $h(0)=0$, $h'(0)=1$ and satisfying the condition $${\real} \left( \frac{z h''(z)}{\alpha h'(z)}\right) <\frac{1}{2} ~\mbox{ for $z\in \ID$,} $$ where $0<\alpha\leq1$. The aim of this article is to show that this family has several elegant properties such as involving Blaschke products, Schwarzian derivative and univalent harmonic mappings.

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Liulan Li, Saminthan Ponnusamy. 2024-07-20. Geometric subfamily of functions convex in some direction and Blaschke products. https://arxiv.org/abs/2407.14922

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