一类微分从属性及其应用(英文)

Some Classes of Differential Subordinations and Their Applications

中文摘要:

      记△={|z|<1}.设函数(?):C~2×△→C在区域D(?)C中解析,G是△中的单叶解析函数.若△中的解析函数p(z)满足微分从属关系(?)(p(z),zp’(z);z)(?)G(z),z∈△,则可确定(?)和G的某些条件使之Re p(z)>p(z∈△),并且给出这些结果的某些应用.

英文摘要:

      Let G be univalent in the unit disc Δ. Let φ:C²×Δ→C be analytic in a domain D?C and let p(z) be analytic in Δ with (p(z), zp′(z);z)∈D when z∈Δ . Assume that p(z) satisfies the differential subordination φ(p(z), zp′(z): z)(?)G(z), z∈A ,(where “(?)”denotes subordination). We determine some conditions on φ and G so that Rep(z)>ρ in Δ and give some applications of these resullts .