Level sets for functions convex in one direction
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- by Johnny E. Brown PDF
- Proc. Amer. Math. Soc. 100 (1987), 442-446 Request permission
Abstract:
Goodman and Saff conjectured that if $f$ is convex in the direction of the imaginary axis then so are the functions $\frac {1}{r}f(rz)$ for all $0 < r < \sqrt 2 - 1$, i.e., the level sets $f(|z| < r)$ are convex in the direction of the imaginary axis for $0 < r < \sqrt 2 - 1$. A weak form of this conjecture is proved and a question of Brannan is answered negatively.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 442-446
- MSC: Primary 30C45
- DOI: https://doi.org/10.1090/S0002-9939-1987-0891142-9
- MathSciNet review: 891142