一阶微分从属关系及其某些应用

FIRT-ORDER DIFFERENTIAL SUBORDINATIONS AND ITS SOME APPLICATIONS TO INTEGRAL OPERATORS

记设函数中解析,G(z)是△中的单叶解析函数。若△中的解析函数P(z)=a+…满足一阶微分从属关系 则根据Φ和G可以导出P(z)的某些性质,利用这些结果,我们讨论一类积分算子,从而得到星象函数的某些充分条件。

Let Δ denote the unit disc {|z|<1}. Suppose that the function ψ. (?)2×Δ→(?) be analytic in a domain Dr3(?) and the function G(z) be univalent inΔ. Let p(z)=a+… be analytic in Δ and satisfies the first-order differential subordjna tionψ(p(z), zp’(z); z)(?)G(z), z∈Δ.We determine conditions on ψ and G so that Rep(z)>ρ in Δ . We also discuss a class of integral operators, and obtain some sufficient conditions for starlike functions.