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Convolution properties of a class of starlike functions. (English) Zbl 0672.30007

The authors study analytic functions \(f(z)=z+a_ 2z^ 2+..\). of the unit disk \({\mathbb{D}}\) for which \[ Re(f'(z)+zf''(z))>0\quad (z\in {\mathbb{D}}). \] They prove for example that if f and g fulfill this condition then so does f*g, which furthermore is convex. Here * denotes Hadamard convolution.
Reviewer: W.Koepf

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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