Level sets for functions convex in one direction

Author:
Johnny E. Brown

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

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Abstract: Goodman and Saff conjectured that if is convex in the direction of the imaginary axis then so are the functions for all , i.e., the level sets are convex in the direction of the imaginary axis for . A weak form of this conjecture is proved and a question of Brannan is answered negatively.

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0891142-9

Article copyright:
© Copyright 1987
American Mathematical Society