从属解析函数族的有限阶哈达玛乘积

Abstract

Abstract:

Let P(A, B) denote a class of analytic functions subordinated to the function 1+Az/1-Bz, where A+B≠0, |B|≤1. The Hadamard product of finitely order of certain classes H ₁, H₂, …, H_n is defined by H₁*H₂*H₃*…*H_n(z)={f₁*f₂*f₃*… f_n(z): f_i ∈H_i, i =1, 2, …, n, n ∈Z⁺}. It obtains the necessary and sufficient conditions for equality P(A₁, B₁)*P(A₂, B₂)*P(A₃, B₃)*…*P(A_n, B_n)=P(X, Y), which extends the corresponding earlier results.

Key words: Analytic function, Hadamard product, Subordination, Necessary and sufficient conditions

CLC Number:

30C45

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XIONG Liang-Peng, LIU Xiao-Li. Hadamard Product of Finitely Order of Certain Class of Analytic Functions Defined by Subordination[J].Acta mathematica scientia,Series A, 2014, 34(1): 150-156.

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Hadamard Product of Finitely Order of Certain Class of Analytic Functions Defined by Subordination

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