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Proceedings of the American Mathematical Society

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

 

 

Uniformly convex functions and a corresponding class of starlike functions


Author: Frode Rønning
Journal: Proc. Amer. Math. Soc. 118 (1993), 189-196
MSC: Primary 30C45; Secondary 30C50
DOI: https://doi.org/10.1090/S0002-9939-1993-1128729-7
MathSciNet review: 1128729
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Abstract: We investigate starlike functions $ f(z) = z + \sum\nolimits_{k = 2}^\infty {{a_k}{z^k}} $ with the property that $ zf'(z)/f(z)$ lies inside a certain parabola. These functions are closely related to a class of functions called uniformly convex and recently introduced by Goodman. We give some particular examples of functions having the required properties, and we give upper bounds on the coefficients and the modulus $ \vert f(z)\vert$ of the functions in the class.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1128729-7
Article copyright: © Copyright 1993 American Mathematical Society