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Convolutions of meromorphic univalent functions with positive coefficients. (English) Zbl 0634.30015

The author considers functions \[ f(z)=z^{- 1}+\sum^{\infty}_{n=1}a_ nz^ n \] with nonnegative coefficients \(a_ n\geq 0,\) \(n\in {\mathbb{N}}\) that are starlike of order \(\alpha,\) and give the order of starlikeness of the convolution \[ f*g(z)=1/z+\sum^{\infty}_{n=1}a_ nb_ nz^ n \] of f with \[ g(z)=1/z+\sum^{\infty}_{n=1}b_ nz^ n. \] The paper contains a lot of misprints.
Reviewer: W.Koepf

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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