检索结果-南通市图书馆

THE SUBORDINATION PRINCIPLE AND ITS APPLICATION TO THE GENERALIZED ROPER-SUFFRIDGE EXTENSION OPERATOR

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2022年第2期42卷 611-622页

作者：王建飞张晓飞 School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China School of Mathematics and Statistics Pingdingshan UniversityPingdingshan 467000China

This note is devoted to applying the principle of subordination in order to explore the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator with special analytic properties.First,we prove that both the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator preserve subordination.As applications,we obtain that if β∈[0,1],γ∈[0,1/r]and β+γ≤1,then the Roper-Suffridge extension operator Φ_(β+γ)(f)(z)=(f(z_(1)),(f(z_(1))/z_(1))^(β)(f’(z_(1)))^(γ)w),z∈Ω_(p,r) preserves an almost starlike mapping of complex order λ on Ω_(p,r)={z=(z_(1),w)∈C×X:|z_(1)|^(p)+‖w‖_(X)^(r)starlike mapping of complex order λ.Finally,we will obtain the lower bound of distortion theorems associated with the Roper-Suffridge extension operator.This subordination principle seems to be a new idea for dealing with the Loewner chain associated with the Roper-Suffridge extension operator,and enables us to generalize many known results from p=2 to 1≤p≤2.

关键词： Biholomorphic mappings starlike mappings subordination Loewner chain

Extension Operators Preserving Biholomorphic mappings on Hartogs Domains

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2023年第2期44卷 307-324页

作者： Yanyan CUI Heju YANG Yuying QIAO College of Mathematics and Statistics Zhoukou Normal UniversityZhoukou 466001HenanChina College of Science Hebei University of Science and TechnologyShijiazhuang 050024China College of Mathematics and Information Science Hebei Normal UniversityShijiazhuang 050024China

In this paper,the authors extend the Roper-Suffridge operator on the generalized Hartogs domains.They mainly research the properties of the extended operator.By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings,they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex orderλ,almost spirallikeness of typeβand orderα,parabolic spirallikeness of typeβand orderρon the Hartogs domains in different conditions.They conclude that the corresponding extension operator preserves the same geometric invariance on the unit ball B^(n) in C^(n).The conclusions provide a new approach to study these geometric mappings in C^(n).

关键词： Roper-Suffridge operator Spirallike mappings starlike mappings

THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2017年第6期37卷 1817-1829页

作者：崔艳艳王朝君刘浩 College of Mathematics and Information Science Hebei Normal University College of Mathematics and Statistics Zhoukou Normal University Institute of Contemporary Mathematics Henan University

In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit bM1 in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spiraJlike mappings in several complex variables.

关键词： spirallike mappings starlike mappings Roper-Suffridge operator

PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2016年第6期36卷 1767-1779页

作者：王朝君崔艳艳刘浩 College of Mathematics and Statistics Zhoukou Normal University College of Mathematics and Statistics Henan University

In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ （β, A, B）, almost starlike mapping of complex order A on Ωn,p2……pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order a, strongly pirallikeness of type β and order a, almost starlikeness of order a on Ωn,p2……pn The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.

关键词： Roper-Suffridge operator spirallike mappings starlike mappings

THE GROWTH THEOREM FOR QUASI-CONVEX mappings IN HILBERT SPACES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2002年第4期22卷 446-450页

作者：冯淑霞刘浩 University of Science and Technology of China Hefei 230026 China Wuhan Institute of Physics and Mathematics Chinese Academy of Science Wuhan 430071 China Department of Mathematics Henan University Kaifeng 475001 China

In this paper, the authors extend the definition of quasi-convex mappings and obtain the corresponding growth theorem-on the unit ball of a complex Hilbert space X.

关键词： starlike mappings convex mappings quasi-convex mappings

The Alexander Type Theorem in Several Complex Variables

在线全文

学校读者我要写书评

暂无评论

Chinese Quarterly Journal of Mathematics 2013年第2期28卷 290-296页

作者： LIU Ai-chao YAN Chun-yan DUAN Xiao-lin LIU Hao Department of Mathematics Huanghuai College Zhumadian 463000 China Department of Math-ematics Xuchang Vocational Technical College Xuchang 461000 China Institute of Mathematics College of Mathematics and Information Science Henan University Kaifeng475004 China

In this paper, the Alexander type theorem in several complex variables is given by using the parametric representation of a kind of starlike mappings. As a corollary, a new method is set up to prove that the Roper-Suf... 详细信息

关键词： starlike mappings parametric representation Roper-Suffridge extension operator

One Note on the Convexity Radius of Holomorphic mappings on the Unit Ball in Cn

在线全文

学校读者我要写书评

暂无评论

Chinese Quarterly Journal of Mathematics 2012年第3期27卷 323-327页

作者： XU Ji-jun WANG Xiao-feng LIU Hao Department of Mathematics Zhengzhou Normal University Zhengzhou Hcnan 450044 China Department of Mathematics and Physics Henan University of Urban Construction Pingdingshan467036. China Institute of Mathematics and Information. Science Henan University Kaifeng 475004 China

In this paper, we prove that: if M is a family which has convexity radius, then the convexity radius for M and the second order item coefficients of every mapping in M are closely related to each other. As an applicat... 详细信息

关键词： starlike mappings growth theorems convex radius

有界星形圆形域上星形映射的参数表示（英文）

在线全文

学校读者我要写书评

暂无评论

Chinese Quarterly Journal of Mathematics 2016年第3期31卷 288-297页

作者：闫春燕张芳芳 Department of Information Engineering Xuchang Vocational and Technical College College of Information Engineering Huanghe Science and Technology College

In this paper,the parametric representation of starlike mappings is given.As a direct application,the growth theorem is set up.Moreover,a character of starlike mappings is obtained.

关键词： starlike mappings parametric representation growth theorem

在线全文

学校读者我要写书评

暂无评论

多复变ε星形映射的系数(英文)

Chinese Quarterly Journal of Mathematics 2015年第3期 416-419页

作者：闫春燕孙林坡安曼 Department of Information Engineering Xuchang Vocational and Technical College Foundation Department Henan Quality Polytechnic School of Mathematics and System Sciences Beihang University

In this paper, we study ε-starlike mappings on the unit ball in Cn, the upper bounds of coefficients of kth item of homogeneous expansion for ε-starlike mappings are obtained.

关键词： starlike mappings convex mappings ε-starlike mappings