In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the d...In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.展开更多
In this article, first, a sufficient condition for a starlike mapping of order a f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f ...In this article, first, a sufficient condition for a starlike mapping of order a f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f is established as well, where f(z) = (f1(z), f2(z),..., fn(z))' is a starlike mapping of order a or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn, and D2fk(0)(z2) /2i= zk(∑l=1^b akzzl), k = 2t l=1 k = 1, 2,..., n. Our result states that the Bieberbaeh conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order α and biholomorphic starlike mappings) is partly proved.展开更多
In this article, first, we establish the Fekete and Szego inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular d...In this article, first, we establish the Fekete and Szego inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.展开更多
This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties.First,we prove that the Roper-Suffridge extension operator preservesϵstarlikeness on the open unit ba...This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties.First,we prove that the Roper-Suffridge extension operator preservesϵstarlikeness on the open unit ball of a complex Banach space C×X,where X is a complex Banach space.This result includes many known results.Secondly,by introducing a new class of almost boundary starlike mappings of orderαon the unit ball B n of C n,we prove that the Roper-Suffridge extension operator preserves almost boundary starlikeness of orderαon B n.Finally,we propose some problems.展开更多
In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known clas...In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered.展开更多
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.
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 dom...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^n-1.Another 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.展开更多
In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of ...In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.展开更多
In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities...In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.展开更多
Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S ...Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.展开更多
In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
In this paper the authors study (1-γ+zf(?)(z)/f'(z))/(zf'(z)/f(z)) as a criteria for starlikeness and convexity. Sharp upper bound of |α2| and of the Fekete-Szego functional |α3-μα22| is given for a class...In this paper the authors study (1-γ+zf(?)(z)/f'(z))/(zf'(z)/f(z)) as a criteria for starlikeness and convexity. Sharp upper bound of |α2| and of the Fekete-Szego functional |α3-μα22| is given for a class of analytic functions defined by using this expression.展开更多
In this paper, using Salagean differential operator, we define and investigate a new subclass of univalent functions . We also establish a characterization property for functions belonging to the class .
In this paper we shall investigate the bound of starlikeness r for the classS(α, n) in [1]. We obtain the following sharp result:where α_0 is the unique solution of the equationα[1+(1-2α)r^(2n)]/1-r^(2n)={1-(1-2α...In this paper we shall investigate the bound of starlikeness r for the classS(α, n) in [1]. We obtain the following sharp result:where α_0 is the unique solution of the equationα[1+(1-2α)r^(2n)]/1-r^(2n)={1-(1-2α)r^n/1+r^n}~2with respect to α in the open interval (0, 1). This result is also the extension of somewell-known ones in [2], [3, Theorem 1] and [4, Theorem 2]展开更多
A function f(z) defined on the unit disc U is said to be logharmonic if it is the solution of the nonlinear elliptic partial differential equation where such that . These mappings admit a global representation of the ...A function f(z) defined on the unit disc U is said to be logharmonic if it is the solution of the nonlinear elliptic partial differential equation where such that . These mappings admit a global representation of the form where In this paper,we shall consider the logharmonic mappings , where is starlike. Distortion theorem and radius of starlikess are obtained. Moreover, we use star functions to determine the integral means for these mappings. An upper bound for the arclength is included.展开更多
Let An(p)(p,n ∈ N = {1,2,3,...}) denote the class of functions of the form f(z) = zp +ap+nzp+n +...which are analytic in the unit disk E = {z:|z| < 1}.A function f(z) in A(p) is said to be in the class Sp(a,b) if ...Let An(p)(p,n ∈ N = {1,2,3,...}) denote the class of functions of the form f(z) = zp +ap+nzp+n +...which are analytic in the unit disk E = {z:|z| < 1}.A function f(z) in A(p) is said to be in the class Sp(a,b) if it satisfies zf(z) pf(z) 1 + az 1 + bz for some a and b(-1 ≤ b < a ≤ 1).In this paper,using the method of differential subordinations,we give new criteria for f(z) to be in the classes Sp(a,b)(-1 ≤ b < a ≤ 1),that is,if f(z) ∈ A(p) satisfies f(z) = 0 in 0 < |z| < 1,f(z) = 0 when μ = 1,and zf(z) f(z) μ 1 + zff((zz)) + λzff(z(z))h(z),where h(z) = p1+μ(1 + λ) 11 ++ abzz 1+μ + pμ(1 + az)1-μ(1+bz)1+μ,λ≥-1,μ∈ {-1,0,1},then f(z) ∈ Sp(a,b).Our results improve or extend some results due to Owa,Nunokawa,Padmanabhan,Silverman,Obradovic,Yang and others[3-10].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 investigated the coefficient estimates and the Fekete-Szegö?problem for the subclass of analytic univalent functions involving the linear transformation Dsα,β,γf for the normalized analyt...In this paper, we investigated the coefficient estimates and the Fekete-Szegö?problem for the subclass of analytic univalent functions involving the linear transformation Dsα,β,γf for the normalized analytic function f (z) = z + a2z2 + a3z3 + … .展开更多
We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the q...We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including integral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.展开更多
基金the National Natural Science Foundation of China(12071354)XIONG was the National Natural Science Foundation of China(12061035)+2 种基金the Jiangxi Provincial Natural Science Foundation(20212BAB201012)the Research Foundation of Jiangxi Provincial Department of Education(GJJ201104)the Research Foundation of Jiangxi Science and Technology Normal University(2021QNBJRC003)。
文摘In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.
基金Project supported by National Natural Science Foundation of China(10971063,11061015)Major Program of Zhejiang Provincial Natural Science Foundation of China(D7080080)Guangdong Natural Science Foundation(06301315)
文摘In this article, first, a sufficient condition for a starlike mapping of order a f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f is established as well, where f(z) = (f1(z), f2(z),..., fn(z))' is a starlike mapping of order a or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn, and D2fk(0)(z2) /2i= zk(∑l=1^b akzzl), k = 2t l=1 k = 1, 2,..., n. Our result states that the Bieberbaeh conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order α and biholomorphic starlike mappings) is partly proved.
基金supported by NNSF of China(11471111,11561030 and 11261022)the Jiangxi Provincial Natural Science Foundation of China(20152ACB20002,20161BAB201019)Natural Science Foundation of Department of Education of Jiangxi Province,China(GJJ150301)
文摘In this article, first, we establish the Fekete and Szego inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.
基金the NNSF of China(11671362,11971165)Beijing Municipal Natural Science Foundation(1182008)the Scientific Research Funds of Huaqiao University.
文摘This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties.First,we prove that the Roper-Suffridge extension operator preservesϵstarlikeness on the open unit ball of a complex Banach space C×X,where X is a complex Banach space.This result includes many known results.Secondly,by introducing a new class of almost boundary starlike mappings of orderαon the unit ball B n of C n,we prove that the Roper-Suffridge extension operator preserves almost boundary starlikeness of orderαon B n.Finally,we propose some problems.
文摘In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered.
基金Supported by the National Natural Science Foundation of China(11271359) Correspond- ing author: AN Man
文摘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.
基金supported by the National Natural Science Foundation of China(11001246,11101139)Zhejiang Innovation Project(T200905)
文摘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^n-1.Another 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.
基金supported by NSF of Zhejiang Province(D7080080, Y6090036, Y6090694, Y6100219)the National Natural Science Foundation of China (10971063,11001246, 11031008, 11101139)
文摘In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.
基金supported by the NNSF of China(11001074,11061015,11101124)the Foundation for University Young Key Teacher of Henan Province
文摘In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.
基金The NSF(11561001)of Chinathe NSF(2014MS0101)of Inner Mongolia Province+1 种基金the Higher School Foundation(NJZY19211)of Inner Mongolia of Chinathe NSF(KJ2018A0839,KJ2018A0833)of Anhui Provincial Department of Education
文摘Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.
文摘In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
文摘In this paper the authors study (1-γ+zf(?)(z)/f'(z))/(zf'(z)/f(z)) as a criteria for starlikeness and convexity. Sharp upper bound of |α2| and of the Fekete-Szego functional |α3-μα22| is given for a class of analytic functions defined by using this expression.
文摘In this paper, using Salagean differential operator, we define and investigate a new subclass of univalent functions . We also establish a characterization property for functions belonging to the class .
文摘In this paper we shall investigate the bound of starlikeness r for the classS(α, n) in [1]. We obtain the following sharp result:where α_0 is the unique solution of the equationα[1+(1-2α)r^(2n)]/1-r^(2n)={1-(1-2α)r^n/1+r^n}~2with respect to α in the open interval (0, 1). This result is also the extension of somewell-known ones in [2], [3, Theorem 1] and [4, Theorem 2]
文摘A function f(z) defined on the unit disc U is said to be logharmonic if it is the solution of the nonlinear elliptic partial differential equation where such that . These mappings admit a global representation of the form where In this paper,we shall consider the logharmonic mappings , where is starlike. Distortion theorem and radius of starlikess are obtained. Moreover, we use star functions to determine the integral means for these mappings. An upper bound for the arclength is included.
基金Supported by the Natural Science Foundation of Jiangsu Education Department(06KJD110003)
文摘Let An(p)(p,n ∈ N = {1,2,3,...}) denote the class of functions of the form f(z) = zp +ap+nzp+n +...which are analytic in the unit disk E = {z:|z| < 1}.A function f(z) in A(p) is said to be in the class Sp(a,b) if it satisfies zf(z) pf(z) 1 + az 1 + bz for some a and b(-1 ≤ b < a ≤ 1).In this paper,using the method of differential subordinations,we give new criteria for f(z) to be in the classes Sp(a,b)(-1 ≤ b < a ≤ 1),that is,if f(z) ∈ A(p) satisfies f(z) = 0 in 0 < |z| < 1,f(z) = 0 when μ = 1,and zf(z) f(z) μ 1 + zff((zz)) + λzff(z(z))h(z),where h(z) = p1+μ(1 + λ) 11 ++ abzz 1+μ + pμ(1 + az)1-μ(1+bz)1+μ,λ≥-1,μ∈ {-1,0,1},then f(z) ∈ Sp(a,b).Our results improve or extend some results due to Owa,Nunokawa,Padmanabhan,Silverman,Obradovic,Yang and others[3-10].
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 investigated the coefficient estimates and the Fekete-Szegö?problem for the subclass of analytic univalent functions involving the linear transformation Dsα,β,γf for the normalized analytic function f (z) = z + a2z2 + a3z3 + … .
基金Supported by National Natural Science Foundation of China(Nos.11971274,12061074,11671344).
文摘We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including integral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.