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The Univalence of a Linear Combination of Convex Mappings

✍ Scribed by MacGregor, T. H.

Book ID
120097008
Publisher
Oxford University Press
Year
1969
Tongue
English
Weight
76 KB
Volume
s1-44
Category
Article
ISSN
0024-6107

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πŸ“œ SIMILAR VOLUMES

On the radius of convexity of linear com
On the radius of convexity of linear combinations of univalent functions and their derivatives
✍ Richard Greiner; Oliver Roth πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 169 KB

## Abstract Let __S__ denote the set of normalized univalent functions in the unit disk. We consider the problem of finding the radius of convexity __r~Ξ±~__ of the set {(1 – __Ξ±__)__f__(__z__) + __Ξ±zf__β€²(__z__) : __f__ ∈ __S__} for fixed __Ξ±__ ∈ β„‚. Using a linearization method we find the exact