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
This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety, where α_ is unique solution of equation (αα)^(1/2)=σwith a in (0.1),and α-[1+(1-2α)r^(2n)]/(1-r^(2n)),σ =[1-(1-2α)r~]...This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety, where α_ is unique solution of equation (αα)^(1/2)=σwith a in (0.1),and α-[1+(1-2α)r^(2n)]/(1-r^(2n)),σ =[1-(1-2α)r~]/(1+r~).Futhermore,we consider an extension of class S(α,n):Let S(α、β、n) denote the class of functions f(z)=z+α_z^(n+1)+…(n≥1)that are analytie in |z|<1 such that f(z)/g (z)∈p(α,n)[1],where g(z)∈S~*(β)[2].This paper prove that the radius of starlikeness of class S(α, β,n) is given by the smallest positive root(less than 1)of the following equations (1-2α)(1-2β)r^(2)-2[1-α-β-n(1-α)]r^+1=0.0≤α≤α_0, (1-α)[1-(1-2β)r~]-n[r^(1+r^)=0.,α_0≤α<1. where α=[1+(1-2α)r^(2)]/(1-r^(2)(0≤r<1),α_0(?(0,1) is some fixed number.This result is also the cxtension of well-known results[T.Th3] and [8,Th3]展开更多
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This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety, where α_ is unique solution of equation (αα)^(1/2)=σwith a in (0.1),and α-[1+(1-2α)r^(2n)]/(1-r^(2n)),σ =[1-(1-2α)r~]/(1+r~).Futhermore,we consider an extension of class S(α,n):Let S(α、β、n) denote the class of functions f(z)=z+α_z^(n+1)+…(n≥1)that are analytie in |z|<1 such that f(z)/g (z)∈p(α,n)[1],where g(z)∈S~*(β)[2].This paper prove that the radius of starlikeness of class S(α, β,n) is given by the smallest positive root(less than 1)of the following equations (1-2α)(1-2β)r^(2)-2[1-α-β-n(1-α)]r^+1=0.0≤α≤α_0, (1-α)[1-(1-2β)r~]-n[r^(1+r^)=0.,α_0≤α<1. where α=[1+(1-2α)r^(2)]/(1-r^(2)(0≤r<1),α_0(?(0,1) is some fixed number.This result is also the cxtension of well-known results[T.Th3] and [8,Th3]
