Published 2004-05-15
Keywords
- hyperbolically convex function,
- distortion theorem,
- modulus of families of curves,
- reduced modulus.
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How to Cite
On distortion under hyperbolically convex maps. (2004). Scientia Series A: Mathematical Sciences, 10, 37-45. https://revistas.usm.cl/scientia/article/view/66
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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