In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almos...In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.展开更多
Let f（x） be an almost spirallike mapping of type β with order B on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f（x）, we also prove that the estimation is...Let f（x） be an almost spirallike mapping of type β with order B on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f（x）, we also prove that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.展开更多
In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x....In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.展开更多
In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.
In this paper, we deduce growth and covering theorem for f（x） by the other means,where f（x） is strongly spirallike mapping of type β with order α defined on Unit Ball B of complex Banach space, and still give gr...In this paper, we deduce growth and covering theorem for f（x） by the other means,where f（x） is strongly spirallike mapping of type β with order α defined on Unit Ball B of complex Banach space, and still give growth upper bound and distortion upper bound for subordinate mapping.展开更多
In this paper we define two classes of quasiconformal mappings, and study theircovering properties by methods of module. We obtain some new results. In the meantime,we give new methods to prove Koebe 1/2 covering theo...In this paper we define two classes of quasiconformal mappings, and study theircovering properties by methods of module. We obtain some new results. In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.展开更多
In this paper, we deduce growth and covering theorem for f（x） by the othermeans where f（x） is strongly spiral-like mapping of type β with order α defined on UnitBall B of complex Banach space and still give gr...In this paper, we deduce growth and covering theorem for f（x） by the othermeans where f（x） is strongly spiral-like mapping of type β with order α defined on UnitBall B of complex Banach space and still give growth upper bound and distortionbound for subordinate mapping.展开更多
Let Ω∈ C^n be a bounded starlike circular domain with 0 ∈ Ω. In this paper, we introduce a class of holomorphic mappings Mg on Ω. Let f（z） be a normalized locally biholomorphic mapping on Ω such that Jf^-1 （z...Let Ω∈ C^n be a bounded starlike circular domain with 0 ∈ Ω. In this paper, we introduce a class of holomorphic mappings Mg on Ω. Let f（z） be a normalized locally biholomorphic mapping on Ω such that Jf^-1 （z） f（z） ∈Mg and z = 0 is the zero of order k＋1 of f（z） - z. We obtain the growth and covering theorems for f（z）. Especially, as corollaries, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown.展开更多
Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and cov...Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^＊k＋1（B）.展开更多
In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients est...In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients estimate,a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings.At last,we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.展开更多
基金The research was supported by the National Nat ural Science Foundation of China(10571164)Specialized Research Fund for the Doctoral Program of Higher Education(20050358052)+1 种基金Guangdong Natural Science Foundation(06301315)the Doctoral Foundation of Zhanjiang Normal University(Z0420)
文摘In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.
基金Supported by the National Natural Science Foundation of China(10271117)
文摘Let f（x） be an almost spirallike mapping of type β with order B on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f（x）, we also prove that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.
基金Foundation item： Supported by the National Natural Science Foundation of china（10571044）
文摘In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.
文摘In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.
文摘In this paper, we deduce growth and covering theorem for f（x） by the other means,where f（x） is strongly spirallike mapping of type β with order α defined on Unit Ball B of complex Banach space, and still give growth upper bound and distortion upper bound for subordinate mapping.
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(04B056)Supported by the Nanhua University Key Items(06Z02)
文摘In this paper we define two classes of quasiconformal mappings, and study theircovering properties by methods of module. We obtain some new results. In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.
基金Supported by the National Natural Science Foundation of China（10571044）
文摘In this paper, we deduce growth and covering theorem for f（x） by the othermeans where f（x） is strongly spiral-like mapping of type β with order α defined on UnitBall B of complex Banach space and still give growth upper bound and distortionbound for subordinate mapping.
基金Supported by NNSF of China(10571164)Supported by SRFDP of Higher Education(20050358052)
文摘Let Ω∈ C^n be a bounded starlike circular domain with 0 ∈ Ω. In this paper, we introduce a class of holomorphic mappings Mg on Ω. Let f（z） be a normalized locally biholomorphic mapping on Ω such that Jf^-1 （z） f（z） ∈Mg and z = 0 is the zero of order k＋1 of f（z） - z. We obtain the growth and covering theorems for f（z）. Especially, as corollaries, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown.
基金Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Nos.19540205,200717540138,2007).
文摘Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^＊k＋1（B）.
基金National Natural Science Foundation of China(Grant No.12071116)the Key Projects of Hunan Provincial Department of Education(Grant No.21A0429)+3 种基金the Discipline Special Research Projects of Hengyang Normal University(Grant No.XKZX21002)the Science and Technology Plan Project of Hunan Province(Grant No.2016TP1020)the Application-Oriented Characterized Disciplines,Double First-Class University Project of Hunan Province(Xiangjiaotong[2018]469)Mathematical Research Impact Centric Support(MATRICS)of the Department of Science and Technology(DST),India(MTR/2017/000367).
文摘In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients estimate,a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings.At last,we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.
