On certain classes of close-to-convex functions
A function f, analytic in the unit disk E and given by , f(z)=z+∑k=2∞anzk is said to be in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1−z)n+1∗f, n∈N0={0,1,2,…} and ∗ denotes the Hadamard product or convolution. The classes Kn are investigated and some properties are given. It i...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000390 |
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| Summary: | A function f, analytic in the unit disk E and given by , f(z)=z+∑k=2∞anzk is said to be
in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1−z)n+1∗f, n∈N0={0,1,2,…}
and ∗ denotes the Hadamard product or convolution. The classes Kn are investigated and some
properties are given. It is shown that Kn+1⫅Kn and Kn consists entirely of univalent functions.
Some closure properties of integral operators defined on Kn are given. |
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| ISSN: | 0161-1712 1687-0425 |