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Proceedings of the American Mathematical Society

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



On $ p$-close-to-star functions of order $ \alpha $

Author: Hassoon S. Al-Amiri
Journal: Proc. Amer. Math. Soc. 29 (1971), 103-108
MSC: Primary 30.42
MathSciNet review: 0281894
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Abstract: In a recent paper M. Finkelstein has used an iterated form of Schwarz's lemma to obtain growth estimates for convex functions and starlike functions of order zero. These estimates involve the second coefficient. W. E. Chase has announced results about the growth estimates and also about a radius of univalence and starlikeness for p-close-to-star functions of order zero. The author generalizes the above results to functions of order $ \alpha $, $ 0 \leqq \alpha \leqq 1$.

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Keywords: Univalent functions, convex functions of order $ \alpha $, starlike functions of order $ \alpha $, p-close-to-star functions of order $ \alpha $, Schwarz lemma, functions of positive real part, radius of univalence, radius of starlikeness
Article copyright: © Copyright 1971 American Mathematical Society

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