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In this paper,the authors establish distortion theorems for various subfamilies H_k(B)of holomorphic mappings defined in the unit ball in C~n with critical points,where k is any positive integer.In particular,the distortion theorem for locally biholomorphic mappings is obtained when k tends to ∞.These distortion theorems give lower bounds on|det f′(z)|and Re det f′(z).As an application of these distortion theorems,the authors give lower and upper bounds of Bloch constants for the subfamiliesβ_k(M)of holomorphic mappings.Moreover,these distortion theorems are sharp.When B is the unit disk in C,these theorems reduce to the results of Liu and Minda.A new distortion result of Re det f′(z)for locally biholomorphie mappings is also obtained. 相似文献
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In this article.a normalized biholomorphic mapping f defined on bounded starlike circular domain in C″is considered,where z=0 is a zero of order k 1 of f(z)(?) The sharp growth.covering theorems for almost starlike mappings of order a and starlile mappings of order wave established.Meanwhile,the construction of the above mappings on bounded starlike circular domain in C~n is also discussed,it provides the extremal mappings for the growth,covering theorems of the above mappings. 相似文献
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In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of |det (f'(z))| and ? det (f'(z)) for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given. 相似文献
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本文定义了ε星形映照族,用统一的观点来处理复Banach空间、Cn及C中的各种区域上的凸映照族与星形映照族,研究它们之间是如何过渡的,并讨论了其判别准则及Roper-Suffridge算子. 相似文献
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The authors establish the coefficient inequalities for a class of
holomorphic mappings on the unit ball in a complex Banach space or
on the unit polydisk in $\mathbb{C}^n$, which are natural extensions
to higher dimensions of some Fekete and Szeg\"o inequalities for
subclasses of the normalized univalent functions in the unit disk. 相似文献
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