Quasiconformal extensions for some geometric subclasses of univalent functions
Let S denote the set of all functions f which are analytic and univalent in the unit disk D normalized so that f(z)=z+a2z2+…. Let S∗ and C be those functions f in S for which f(D) is starlike and convex, respectively. For 0≤k<1, let Sk denote the subclass of functions in S which admit (1+k)/(1−k)...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000193 |
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| Summary: | Let S denote the set of all functions f which are analytic and univalent in the unit disk D normalized so that f(z)=z+a2z2+…. Let S∗ and C be those functions f in S for which f(D) is starlike and convex, respectively. For 0≤k<1, let Sk denote the subclass of functions in S which admit (1+k)/(1−k)-quasiconformal extensions to the extended complex plane. Sufficient conditions are given so that a function f belongs to Sk⋂S∗ or Sk⋂C. Functions whose derivatives lie in a half-plane are also considered and a Noshiro-Warschawski-Wolff type sufficiency condition is given to determine which of these functions belong to Sk. From the main results several other sufficient conditions are deduced which include a generalization of a recent result of Fait, Krzyz and Zygmunt. |
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| ISSN: | 0161-1712 1687-0425 |