Zhu, Yu-Can; Liu, Ming-Sheng Second order differential subordinations of holomorphic mappings on bounded convex balanced domains in \(\mathbb C^n\). (English) Zbl 1137.32009 JIPAM, J. Inequal. Pure Appl. Math. 8, No. 4, Paper No. 104, 15 p. (2007). Summary: In this paper, we obtain some second order differential subordinations of holomorphic mappings on a bounded convex balanced domain \(\Omega\) in \(\mathbb{C}^n\). These results imply some first order differential subordinations of holomorphic mappings on a bounded convex balanced domain \(\Omega\) in \(\mathbb{C}^n\). When \(\Omega\) is the unit disc in the complex plane \(\mathbb{C}\), these results are just the ones of Miller and Mocanu et al. about differential subordinations of analytic functions on the unit disc in the complex plane \(\mathbb{C}\). MSC: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:differential subordination; biholomorphic convex mapping; convex balanced domain; Minkowski functional PDFBibTeX XMLCite \textit{Y.-C. Zhu} and \textit{M.-S. Liu}, JIPAM, J. Inequal. Pure Appl. Math. 8, No. 4, Paper No. 104, 15 p. (2007; Zbl 1137.32009) Full Text: EuDML EMIS