一函数族的从属关系

SUBORDINATION FOR A CLASS OF FUNCTIONS

通过考察一比较大的函数族,获得了一般性从属定理,特别对任何函数F(z)∈J(α,β)(α≥0,β≥0),成立关系F(z)/z<(Kα(β,z))/z,此结果包含了Brickman L猜测.

By studing a larger class of functions, a general subordination theorem is obtained, especially the relation of F(z)/z<Ka(β,z)/z is tenable for any function F(z) ∈J(α,β), where α≥0,β≥1. This result includes L. Brickman' s conjecture.