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arXiv · 1201.4475

Biholomorphic Convex Mappings of Order alpha on the Unit Ball in Hilbert Spaces

Ming-Sheng Liu·Yu-Can Zhu
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Abstract

In this paper, we first introduce the concept of biholomorphic convex mapping of order alpha on the unit ball B in a complex Hilbert space X. Next we provide some sufficient conditions that a locally biholomorphic mapping f is a biholomorphic convex mapping of order alpha and give an Alexander's theorem between the subclass of convex mappings and the subclass of starlike mappings on B in Hilbert space. We also obtain the order of starlikeness of biholomorphic convex mappings of order alpha on B in Hilbert spaces. Finally, we construct some concrete examples of biholomorphic convex mappings of order alpha on B in Hilbert spaces by means of a linear operator.

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Ming-Sheng Liu, Yu-Can Zhu. 2012-01-21. Biholomorphic Convex Mappings of Order alpha on the Unit Ball in Hilbert Spaces. https://arxiv.org/abs/1201.4475

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