2012/01/21 by Ming-Sheng Liu, Liu, Ming-Sheng, Yu-Can Zhu +1
Mathematics · #30C45 #32H02 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:30C45 #msc:32H02
paper · pdf · doi:10.48550/arxiv.1201.4475
15 pages
arxiv created 2012/01/21 · arxiv updated 2012/01/24
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.