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Proceedings of the American Mathematical Society

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

 
 

 

New criteria for univalent functions


Author: Stephan Ruscheweyh
Journal: Proc. Amer. Math. Soc. 49 (1975), 109-115
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1975-0367176-1
MathSciNet review: 0367176
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Abstract: The classes $ {K_n}$ of functions $ f(z)$ regular in the unit disc $ \mathfrak{U}$ with $ f(0) = 0,f'(0) = 1$ satisfying

$\displaystyle \operatorname{Re} [{({z^n}f)^{(n + 1)}}/{({z^{n - 1}}f)^{(n)}}] > (n + 1)/2$

in $ \mathfrak{U}$ are considered and $ {K_{n + 1}} \subset {K_n},n = 0,1, \cdots $, is proved. Since $ {K_0}$ is the class of functions starlike of order 1/2 all functions in $ {K_n}$ are univalent. Some coefficient estimates are given and special elements of $ {K_n}$ are determined.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0367176-1
Keywords: Univalent functions, starlike and convex functions, coefficient estimates, Hadamard product
Article copyright: © Copyright 1975 American Mathematical Society

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