Let A denote the class of funetions f(z) defined by f(z)=z-sum from n=2 to ∞a_nz^n (a_n>0) (1) which are analytic in the unit disk U= {z:|z|<1}. A function f(z)∈A is said to be in the class S (x,β,γ), if and...Let A denote the class of funetions f(z) defined by f(z)=z-sum from n=2 to ∞a_nz^n (a_n>0) (1) which are analytic in the unit disk U= {z:|z|<1}. A function f(z)∈A is said to be in the class S (x,β,γ), if and only if |(f′(z)-1)/(af′(z)+1-(1+α)β)|<γ(2) for 0<x<1, 0<β<1, and 0<<1.展开更多
Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))...Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.展开更多
In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
Let p~*(A,B,k,a,β) be the class of functions f(z)=a_1-sum from n=k to ∞(|a_n|Z^n) (a_1>0,k≥2) regular and univalent in the unit disc U={z:|z|<1}and satis-fying where and We denote by P_o(A,B,k, α,β,z_o) and...Let p~*(A,B,k,a,β) be the class of functions f(z)=a_1-sum from n=k to ∞(|a_n|Z^n) (a_1>0,k≥2) regular and univalent in the unit disc U={z:|z|<1}and satis-fying where and We denote by P_o(A,B,k, α,β,z_o) and p_1(A,k,α,β,z_o), two suoclasses of p~*(A,B,k,α,β), consisting of the functions which satisfy f(z_n)=z_n and f′(z_n)=1,respectively, here In this paper we obtain ooefficient estimates,distortion and closure theorems and radius of convexity of order p (0≤ρ<1)for the classes P_o(A,B,k, α,β,z_0) and P_1(A,B,k,α,β,z_o).展开更多
In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
文摘Let A denote the class of funetions f(z) defined by f(z)=z-sum from n=2 to ∞a_nz^n (a_n>0) (1) which are analytic in the unit disk U= {z:|z|<1}. A function f(z)∈A is said to be in the class S (x,β,γ), if and only if |(f′(z)-1)/(af′(z)+1-(1+α)β)|<γ(2) for 0<x<1, 0<β<1, and 0<<1.
文摘Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
文摘Let p~*(A,B,k,a,β) be the class of functions f(z)=a_1-sum from n=k to ∞(|a_n|Z^n) (a_1>0,k≥2) regular and univalent in the unit disc U={z:|z|<1}and satis-fying where and We denote by P_o(A,B,k, α,β,z_o) and p_1(A,k,α,β,z_o), two suoclasses of p~*(A,B,k,α,β), consisting of the functions which satisfy f(z_n)=z_n and f′(z_n)=1,respectively, here In this paper we obtain ooefficient estimates,distortion and closure theorems and radius of convexity of order p (0≤ρ<1)for the classes P_o(A,B,k, α,β,z_0) and P_1(A,B,k,α,β,z_o).
文摘In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
