Let U denote the unit disc {z: |z| < 1}. A function f analytic in U, f(o) = 0, is said to be starlike of order α, 0 ≤ α < 1, written as f ∈ S~*(α), iff Re{zf′(z)/f(z)} > α and f is said to be convex of order α, written as f ∈ K(α), iff zf ?(z) ∈ S~*(α) i.e. Re{1 + (zf″(z)/f′(z))} > α for z ∈ U.
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机译：令U表示单位盘{z：| z | <1}。 U中解析的函数f（f（o）= 0）被认为是阶α，0≤α<1的星形，写为f∈S〜*（α），iff Re {zf'（z）/ f （z）}>α，并且说f是阶α的凸，写为f∈K（α），当zf？（z）∈S〜*（α）即Re {1 +（zf''（z ）/ f′（z））}>对于z∈U.
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