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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convex functions with restricted curvature


Authors: D. Styer and D. J. Wright
Journal: Proc. Amer. Math. Soc. 109 (1990), 981-990
MSC: Primary 30C45; Secondary 30C25
DOI: https://doi.org/10.1090/S0002-9939-1990-1010002-6
MathSciNet review: 1010002
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Abstract: Given $ 0 \leq {R_1} \leq {R_2} \leq \infty $, we consider a class of normalized convex functions $ f$ in the unit disk $ {\mathbf{D}}$, for which $ \partial f({\mathbf{D}})$ satisfies a Blaschke Rolling Theorem condition with radii $ {R_1}$ and $ {R_2}$. This class contains the convex functions of bounded type. We study the geometry of the image region $ f({\mathbf{D}})$ and various covering and distortion properties.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1010002-6
Article copyright: © Copyright 1990 American Mathematical Society