کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4616165 | 1339340 | 2014 | 21 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Growth, distortion and coefficient bounds for Carathéodory families in CnCn and complex Banach spaces Growth, distortion and coefficient bounds for Carathéodory families in CnCn and complex Banach spaces](/preview/png/4616165.png)
Let X be a complex Banach space with the unit ball B . The family MM is a natural generalization to complex Banach spaces of the well-known Carathéodory family of functions with positive real part on the unit disc. We consider subfamilies MgMg of MM depending on a univalent function g . We obtain growth theorems and coefficient bounds for holomorphic mappings in MgMg, including some sharp improvements of existing results. When g is convex, we study the family RgRg consisting of holomorphic mappings f:B→Xf:B→X which have the property that the mapping Df(z)(z)Df(z)(z) belongs to MgMg. Further, we consider radius problems related to the family RgRg, when X is a complex Hilbert space. In particular, if X is the Euclidean space CnCn, we obtain some quasiconformal extension results for mappings in RgRg. We also obtain some sufficient conditions for univalence and starlikeness in complex Banach spaces.
Journal: Journal of Mathematical Analysis and Applications - Volume 416, Issue 1, 1 August 2014, Pages 449–469