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New distortion theorems for functions of positive real part and applications to the partial sums of univalent convex functions


Author: S. D. Bernardi
Journal: Proc. Amer. Math. Soc. 45 (1974), 113-118
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1974-0357755-9
MathSciNet review: 0357755
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Abstract: New distortion theorems are obtained for the class of functions $ p(z) = 1 + {c_n}{z^n} + \cdots (n \geq 1)$ which are analytic and Re$ p(z) > \alpha (0 \leq \alpha < 1)$ in the unit disk $ \vert z\vert < 1$. These are used to obtain new results regarding the partial sums of univalent convex functions.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0357755-9
Keywords: Univalent functions, convex functions, radius of starlikeness, functions with positive real part
Article copyright: © Copyright 1974 American Mathematical Society

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