Convex functions with restricted curvature
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- by D. Styer and D. J. Wright PDF
- Proc. Amer. Math. Soc. 109 (1990), 981-990 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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