关于某些具有固定第二系数的单叶函数类

ON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS WITH FIXED SECOND COEFFICIENTS

本文引进Bazilevic函数类的两个子类B(σ,β,b)和B_1(σ,β),研究当F(z)分别属于具有固定第二系数的函数类B(σ,β,b)或B_1(σ.β)时函数的映照性质。此外,我们求得具有固定第二系数的星象函数类S·的α—凸性半径。

Certain subclasses B(σ,β,b)and B1(σ,β) of Bazilevic Functions of type σ,σ>0. are introduced. The object of the present paper is to study the mapping properties of f :when F belongs to B(σ,β,b) or B1 (σ, β) ,with fixed second coefficient. In addition. the radius of α - convexity for starlike functions with fixed second coefficient is obtained. All results are sharp.