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On the Radius of Univalence of the Partial Sums of Convex Functions

โœ Scribed by Ruscheweyh, S.

Book ID
120094451
Publisher
Oxford University Press
Year
1972
Tongue
English
Weight
58 KB
Volume
4
Category
Article
ISSN
0024-6093

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๐Ÿ“œ SIMILAR VOLUMES

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Let f z szqร a z be the sequence of partial sums of a function a z that is analytic in z -1 and either starlike of order โฃ or ks 2 k ร„ 4 convex of order โฃ, 0 F โฃ -1. When the coefficients a are ''small,'' we deterk ร„ ลฝ . ลฝ 4 ร„ ลฝ . ลฝ .4 ร„ ลฝ . X ลฝ .4 mine lower bounds on Re f z rf z , Re f z rf z , R

On the radius of convexity of linear com
On the radius of convexity of linear combinations of univalent functions and their derivatives
โœ Richard Greiner; Oliver Roth ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 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~ฮฑ~__ of the set {(1 โ€“ __ฮฑ__)__f__(__z__) + __ฮฑzf__โ€ฒ(__z__) : __f__ โˆˆ __S__} for fixed __ฮฑ__ โˆˆ โ„‚. Using a linearization method we find the exact