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Uniformly Convex Functions and a Corresponding Class of Starlike Functions
Proceedings of the American Mathematical Society
Vol. 118, No. 1 (May, 1993), pp. 189-196
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160026
Page Count: 8
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We investigate starlike functions f(z) = z + ∑∞ k = 2 akz 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 |f(z)| of the functions in the class.
Proceedings of the American Mathematical Society © 1993 American Mathematical Society