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 paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.
In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it....In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it. This type of domain on which we discuss is rather general,in the sense that the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it.展开更多
The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if ...The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.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 article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the appl...In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established.展开更多
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 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
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 applica...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 application, we show that the convexity radius of starlike mappings r（S＊） 〈 2-3～（1/2）.展开更多
In this paper,the parametric representation of a kind of spirallike mappings is given. As a direct application,the growth Theorem is set up. Moreover,a character of starlike mappings and a kind of spirallike mappings ...In this paper,the parametric representation of a kind of spirallike mappings is given. As a direct application,the growth Theorem is set up. Moreover,a character of starlike mappings and a kind of spirallike mappings is obtained.展开更多
Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a spiral-like mapping of type a on Ω, then f can be expressed as a ...Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a spiral-like mapping of type a on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up.展开更多
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.
In this paper we consider the class ∑^＊（p,α,β,k,c） consisting of analytic functions with negativecoefficients and fixed second coefficient. The object of the present paper is to give coefficient estimates, conve...In this paper we consider the class ∑^＊（p,α,β,k,c） consisting of analytic functions with negativecoefficients and fixed second coefficient. The object of the present paper is to give coefficient estimates, convex linear combinations, some distortion theorems and radii of starlikeness and convexity for f（z） in the class ∑^＊（p,α,β,k,c） .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
We introduce the class of strongly close-to-convex mappings of order c~ in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a comp...We introduce the class of strongly close-to-convex mappings of order c~ in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a complex Hilbert space X or the unit polydisc in Cn. As an application, a sharp growth theorem for strongly close-to-convex mappings of order α is obtained.展开更多
The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain mus...The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.展开更多
This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k-ST(α).We introduce new subclasses of starlike(spirallike)functions,namely,S^(p)_(c)(k,α)(S^(p)_(c)(k,...This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k-ST(α).We introduce new subclasses of starlike(spirallike)functions,namely,S^(p)_(c)(k,α)(S^(p)_(c)(k,α,β)),and discuss their coefficient estimates and the Fekete–Szego–Goluzin’s problem.Then we generalize S^(p)_(c)(k,α,β)on the unit ball B^(n) in C^(n),that is,k-conic spirallike mappings of typeβand orderα.We obtain the growth,covering and distortion theorems of the generalized mappings.Besides that,we construct k-conic spirallike mappings of typeβand orderαon B^(n) through S_(c)(k,α,β)by the generalized Roper-Suffridge extension operators.展开更多
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）.
文摘In this paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.
文摘In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it. This type of domain on which we discuss is rather general,in the sense that the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it.
文摘The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.
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.
基金Supported by the Doctoral Foundation of Pingdingshan University（PXY-BSQD-20150 05） Supported by the Natural Science Foundation of Zhejiang Province（Y14A010047）+1 种基金 Supported by the the Key Scientific Research Projects in Universities of Henan Province（16Bl10010） Supported by the Foster Foundation of Pingdingshan University（PXY-PYJJ2016007）
文摘In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established.
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 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.
文摘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 application, we show that the convexity radius of starlike mappings r（S＊） 〈 2-3～（1/2）.
文摘In this paper,the parametric representation of a kind of spirallike mappings is given. As a direct application,the growth Theorem is set up. Moreover,a character of starlike mappings and a kind of spirallike mappings is obtained.
文摘Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a spiral-like mapping of type a on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up.
基金Supported by the National Natural Science Foundation of China(11271359)
文摘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.
基金The work is supported by UKM grant ST-028-2003 IRPA grant 09-02-02-80 EA208, Malysia.
文摘In this paper we consider the class ∑^＊（p,α,β,k,c） consisting of analytic functions with negativecoefficients and fixed second coefficient. The object of the present paper is to give coefficient estimates, convex linear combinations, some distortion theorems and radii of starlikeness and convexity for f（z） in the class ∑^＊（p,α,β,k,c） .
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.
文摘We introduce the class of strongly close-to-convex mappings of order c~ in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a complex Hilbert space X or the unit polydisc in Cn. As an application, a sharp growth theorem for strongly close-to-convex mappings of order α is obtained.
文摘The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.
基金Supported by NSF of China(Grant Nos.11571089,11871191)Science and Technology Research Projects of He’nan Provincial Education Department(Grant No.17A110041)+1 种基金the key Foundation of Hebei Normal University(Grant No.L2018Z01)Scientific Research Fund of High Level Talents of Zhoukou Normal University(Grant No.ZKNUC2019004)。
文摘This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k-ST(α).We introduce new subclasses of starlike(spirallike)functions,namely,S^(p)_(c)(k,α)(S^(p)_(c)(k,α,β)),and discuss their coefficient estimates and the Fekete–Szego–Goluzin’s problem.Then we generalize S^(p)_(c)(k,α,β)on the unit ball B^(n) in C^(n),that is,k-conic spirallike mappings of typeβand orderα.We obtain the growth,covering and distortion theorems of the generalized mappings.Besides that,we construct k-conic spirallike mappings of typeβand orderαon B^(n) through S_(c)(k,α,β)by the generalized Roper-Suffridge extension operators.
