Extreme Points of Univalent Functions With Two Fixed Points
✍ Scribed by Herb Silverman
- Book ID
- 125682733
- Publisher
- American Mathematical Society
- Year
- 1976
- Tongue
- English
- Weight
- 297 KB
- Volume
- 219
- Category
- Article
- ISSN
- 0002-9947
- DOI
- 10.2307/1997604
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📜 SIMILAR VOLUMES
In this paper a new class of meromorphic univalent functions in terms of an integral operator is defined. We find some properties of this new class by using two fixed points.
For 0p -1, let S denote the class of functions f z meromorphic univalent p Ž . Ž . Ž . in the unit disk ބ with the normalization f 0 s 0, f Ј 0 s 1, and f p s ϱ. Let Ž . S a be the subclass of S with the fixed residue a. In this note we determine the p p Ž . extreme points of the class S a . As a
We discuss two-point distortion inequalities for (not necessarily normalized) univalent functions f on the unit disk D. By a two-point distortion inequality we mean an upper or lower bound on the Euclidean distance |f(a) -f(b)| in terms of d D (a; b), the hyperbolic distance between a and b, and the