کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616165 1339340 2014 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Growth, distortion and coefficient bounds for Carathéodory families in CnCn and complex Banach spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Growth, distortion and coefficient bounds for Carathéodory families in CnCn and complex Banach spaces
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 416, Issue 1, 1 August 2014, Pages 449–469
نویسندگان
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