×

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
PDFBibTeX XMLCite
Full Text: DOI

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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.