In this paper, we obtain the estimates of all homogeneous expansions for a subclass of bi- holomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establ...In this paper, we obtain the estimates of all homogeneous expansions for a subclass of bi- holomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.展开更多
Let Sα*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class Sα*, and then we generalize this result to the un...Let Sα*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class Sα*, and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in Cn.展开更多
In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n）...In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.展开更多
In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme poin...In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball Bn respectively.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11471111)Guangdong Natural Science Foundation(Grant No.2014A030307016)
文摘In this paper, we obtain the estimates of all homogeneous expansions for a subclass of bi- holomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.
基金Supported by NNSF of China(Grant Nos.11561030,11471111 and 11261022)the Jiangxi Provincial Natural Science Foundation of China(Grant Nos.20152ACB20002 and 20161BAB201019)Natural Science Foundation of Department of Education of Jiangxi Province,China(Grant No.GJJ150301)
文摘Let Sα*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class Sα*, and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in Cn.
基金supported by NNSF of China (Grant No.10826083)supported by NNSF of China (Grant No.10571164)+1 种基金NSF of Zhejiang province (Grant No.D7080080)SRFDP of Higher Education (Grant No.20050358052)
文摘In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11101139,11031008,11301136,11571089,11401159 and 11501198)the Science Foundation of Hebei Province(Grant No.A2014205069)+3 种基金the Key Scientific Research Pro jects in Universities of He’nan Province(Grant No.16B110010)the Doctoral Foundation of Pingdingshan University(Grant No.PXY-BSQD-2015005)the Doctoral Foundation of Hebei Normal University(Grant No.L2015B04)the Foster Foundation of Pingdingshan University(Grant No.PXYPYJJ2016007)
文摘In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball Bn respectively.
