On distortion under hyperbolically convex maps

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Published: 2025-08-08
DOI: https://doi.org/10.71712/
Keywords:
hyperbolically convex function, distortion theorem, modulus of families of curves, reduced modulus.

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Alexander Vasil'ev
Departamento de Matemática Universidad Técnica Federico Santa María, Valparaíso, Chile

Abstract

We study the class of hyperbolically convex bounded univalent functions with a boundary normalization in the unit disk U. In the paper we obtain the lower estimate for the distortion in this class. A two-point distortion theorem is also proved. The method of proofs is based on the reduced modulus of digons and the modulus of annuli.

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Vol. 10 (2004)

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Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

On distortion under hyperbolically convex maps (A. Vasil'ev, Trans.). (2025). Scientia Series A: Mathematical Sciences, 10, 37-45. https://doi.org/10.71712/