上半平面中解析函数的微分从属和微分超从属

Differential Subordination and Differential Superordination for Analytic Functions in the Upper Half-Plane

设Ω为复平面C上的任意子集,函数p在上半平面△={z:z∈C和Im(z)>0}内解析,且设Ψ:C^3×△→C.该文建立了上半平面△内满足下列二阶微分超从属条件Ω∈{Ψ(p(z),p′(z),p″(z);z):z∈△}的函数p的基本理论.作为该理论的应用,该文还得到了△内解析函数的某些微分从属和微分超从属结果.

Let Ω be a set in the complex plane C.Also let p be analytic in the upper halfplane Δ = {z：z ∈ C and Im（z） 〉0} and suppose that Ψ：C^3 × Δ→ C.In this paper,we consider the problem of determining properties of functions p that satisfy the following differential superordinationΩ∈{Ψ（p（z）,P′{z）,p″（z）;z）：z∈Δ}.Applications of these results to differential subordination and differential superordination for analytic functions in Δ are also presented.