Abstract
In this paper, we first give the definition of biholomorphic convex mappings of order \(\alpha \) on the Reinhardt domain \(D_{p}^n\) in \(C^{n}\). Next, we provide several sufficient conditions for it. Then we introduce a subclass \(SK(D_{p}^n, \alpha )\) of biholomorphic convex mappings of order \(\alpha \) on \(D_{p}^n\), and give a necessary and sufficient condition for the subclass \(SK(D_{p}^n, \alpha )\). From these, we construct some concrete examples of biholomorphic convex mappings of order \(\alpha \) on \(D_{p}^n\). The results presented extend the related results of earlier authors.
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Communicated by Tao Qian.
This research is supported by Guangdong Natural Science Foundation (Grant Nos. 2014A030307016, 2014A030313422).
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Liu, MS., Li, N. & Yang, Y. On the Biholomorphic Convex Mappings of Order Alpha on \(D_p^n\) . Complex Anal. Oper. Theory 11, 243–260 (2017). https://doi.org/10.1007/s11785-015-0528-x
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DOI: https://doi.org/10.1007/s11785-015-0528-x
Keywords
- Locally biholomorphic mapping
- Biholomorphic convex mapping
- Biholomorphic convex mapping of order \(\alpha \)
- Reinhardt domain \(D_{p}^n\)