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MODIFIED ROPER-SUFFRIDGE OPERATOR FOR SOME SUBCLASSES OF starlike mappings ON REINHARDT DOMAINS

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Acta Mathematica Scientia 2013年第6期33卷 1627-1638页

作者：王建飞 Department of Mathematics and Physics Information EngineeringZhejiang Normal University

In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^*** condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.

关键词： biholomorphic mappings Roper-Suffridge extension operator Reinhardt do-mains starlike mappings homogeneous polynomial of degree m

On the Second-order Item Coefficients for ε-starlike mappings in C^n

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Chinese Quarterly Journal of Mathematics 2002年第4期17卷 78-82页

作者：尹清杰罗萍河南工业职业技术学院基础部河南南阳473009

Let B n be the unit ball in C n, we study ε-starlike mappings on B n. The upper bounds of second order item coefficients of homogeneous expansion for ε-starlike mappings are obtained.

关键词： starlike mappings homogeneous expansion

The Parametric Representation for starlike mappings on Bounded starlike Circular Domains

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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 *** a direct application,the growth theorem is set ***,a character of starlike mappings is obtained.

关键词： starlike mappings parametric representation growth theorem

On the Coefficients Problem of Quasi-convex mappings and starlike Mapppings in C^n

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Chinese Quarterly Journal of Mathematics 2003年第4期18卷 419-424页

作者：刘维先王予民 MathsTeachingandResearchSection HenanPoly-technicalInstitutesNanyang473009China

Let B^n be the unit ball in C^n, we study quasi-convex mappings and starlike mappings on B^n. The upper bounds of second order item coefficients ofr quasi-convex mappings and starlike mappings are obtained.

关键词： starlike mappings quasi-convex mappings convex mappings

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

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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

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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

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

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

作者： Jianfei WANG Xiaofei ZHANG 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 ***,we prove that both the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator preserve *** 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 *** 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

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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 *** mainly research the properties of the extended *** 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 *** 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