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Löwner chains and a subclass of biholomorphic mappings |
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| Authors: | Qing-Hua Xu |
| Affiliation: | a Department of Mathematics, JiangXi Normal University, NanChang 330027, China b Department of Mathematics, Huzhou Teacher's College, Huzhou 313000, China c Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
| Abstract: | In this paper, we give characterization of almost starlike functions of order α (respectively almost starlike mappings of order α) on the unit disc in C (respectively the unit ball in a finite-dimensional complex Banach space) in terms of Löwner chains. Furthermore, using the properties of Löwner chains, we can easily prove that two classes of generalized Roper-Suffridge extension operators preserve almost starlikeness of order α on two important classes of Reinhardt domains in Cn, respectively. |
| Keywords: | Lö wner chains Roper-Suffridge extension operator Starlike mapping Spirallike mapping of type α Almost starlike mappings of order α Reinhardt domain |
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