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arXiv · 2308.08385

A Characterization of concave mappings

V. Bravo·R. Hernández·O. Venegas
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Abstract

This study focuses on Concave mappings, a class of univalent functions that exhibit a unique property: they map the unit disk onto a domain whose complement is convex. The main objective of this work is to characterize these mappings in terms of the real part of the expression $1 +zf''(z)/f'(z)$, considering scenarios where the omitted convex domain is either bounded or unbounded. In the case of a bounded convex domain, we investigate the pivotal role played by the Schwarzian derivative and the order of the functions in understanding the behavior and properties of these mappings.

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V. Bravo, R. Hernández, O. Venegas. 2023-08-16. A Characterization of concave mappings. https://arxiv.org/abs/2308.08385

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