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Media type:
E-Article
Title:
Uniformly convex functions and a corresponding class of starlike functions
Contributor:
Rønning, Frode
Published:
American Mathematical Society (AMS), 1993
Published in:
Proceedings of the American Mathematical Society, 118 (1993) 1, Seite 189-196
Language:
English
DOI:
10.1090/s0002-9939-1993-1128729-7
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
We investigate starlike functions f ( z ) = z + ∑ k = 2 ∞ a k z k f(z) = z + \sum \nolimits _{k = 2}^\infty {{a_k}{z^k}} with the property that z f ′ ( z ) / f ( z ) 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 | f ( z ) | |f(z)| of the functions in the class.