Construction of biholomorphic convex mappings of order \(\alpha\) on \(B_p^n\). (English) Zbl 1474.32038
Summary: Some sufficient conditions for biholomorphic convex mappings of order \(\alpha\) on the Reinhardt domain \(B_p^n\) in \(C^n\) are given; from that, criteria for biholomorphic convex mappings of order \(\alpha\) with particular form become direct. As applications of these sufficient conditions, some concrete biholomorphic convex mappings of order \(\alpha\) on \(B_p^n\) are provided.
MSC:
| 32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
| 32A30 | Other generalizations of function theory of one complex variable |
References:
| [1] | Kohr, G., On some alpha convex mappings on the unit ball of \(C^n\), Demonstratio Mathematica, 31, 1, 209-222 (1998) · Zbl 0910.32023 |
| [2] | Liu, H.; Lu, K.-P., Two subclasses of starlike mappings in several complex variables, Chinese Annals of Mathematics A, 21, 5, 533-546 (2000) · Zbl 1002.32008 |
| [3] | Liu, M. -S., Biholomorphic convex mappings of order \(α\) on \(B_p^n\), Complex Variables and Elliptic Equations, 58, 7, 899-908 (2013) · Zbl 1277.32001 |
| [4] | Liu, M.-S.; Zhu, Y.-C., Biholomorphic convex mappings of order \(\alpha\) on the unit ball in Hilbert spaces, Journal of Mathematical Analysis and Applications, 406, 1, 75-85 (2013) · Zbl 1307.32004 · doi:10.1016/j.jmaa.2013.04.043 |
| [5] | Zhu, Y. C., \( \alpha \)-convex mappings on \(B_P\), Acta Mathematica Scientia A, 25, 1, 84-92 (2005) · Zbl 1065.32009 |
| [6] | Liu, M.-S.; Tang, X.-M., Sufficient conditions for \(ε\) quasi-convex mappings in a complex Banach space, Complex Variables and Elliptic Equations, 58, 9, 1273-1282 (2013) · Zbl 1277.32003 |
| [7] | Roper, K. A.; Suffridge, T. J., Convex mappings on the unit ball of \(C^n\), Journal d’Analyse Mathématique, 65, 333-347 (1995) · Zbl 0846.32006 · doi:10.1007/BF02788776 |
| [8] | Roper, K. A.; Suffridge, T. J., Convexity properties of holomorphic mappings in \(C^n\), Transactions of the American Mathematical Society, 351, 1803-1833 (1999) · Zbl 0926.32012 |
| [9] | Liu, M.-S.; Zhu, Y.-C., Some sufficient conditions for biholomorphic convex mappings on \(B_p^n\), Journal of Mathematical Analysis and Applications, 316, 1, 210-228 (2006) · Zbl 1092.32012 · doi:10.1016/j.jmaa.2005.04.063 |
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