A New Roper-Suffridge Extension Operator on a Reinhardt Domain
We introduce a new Roper-Suffridge extension operator on the following Reinhardt domain given by where f is a normalized locally biholomorphic function on the unit disc D, pj are positive integer, aj are complex constants, and j=2,…,n. Some conditions for aj are f...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/865496 |
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| Summary: | We introduce a new Roper-Suffridge extension operator on the following Reinhardt domain
given by where f is a normalized locally biholomorphic function on the unit disc D, pj are positive integer, aj are complex constants, and j=2,…,n. Some conditions for aj are found under which the operator preserves almost starlike mappings of order α and starlike mappings of order α, respectively. In particular, our results reduce to many well-known results when all αj=0. |
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| ISSN: | 1085-3375 1687-0409 |