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Certain subclasses of univalent functions with fixed second coefficient
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pokhilevich, V. A. |
| Copyright Year | 1986 |
| Abstract | which are regular and univalent on the unit disk E = {z, Izl < i} and whose coefficient c 2 = 2~ in the expansion (3) is fixed, ~E [0, I); the subclass of these functions which, in addition, map E onto regions which are star-shaped with respect to w~ = f(0) = 0 is ~tenoted by S*(2e), and the subclass of those which have bounded rotation is denoted by Ui~. The point z = re ~E E is also fixed. As a corollary, we also obtain the respective limits of convexity of S*(2~) and U(~) [for the class U(~), the coefficient 2~ in (3) must be replaced by ~]. We show that arcs of level lines can be convex (concave) outside of a disk of radius of convexity depending on Rezf~/f~ and Ref~, respectively, for U(~). |
| Starting Page | 559 |
| Ending Page | 562 |
| Page Count | 4 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/BF01060953 |
| Volume Number | 38 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/BF01060953 |
| Alternate Webpage(s) | https://doi.org/10.1007/BF01060953 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
