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Harmonic functions starlike in the unit disk. (English) Zbl 0940.30003
An objective of this note is to study properties of sense preserving harmonic mappings \(f(z)= z+ a_2z^2+\cdots+ b_1\overline z+\cdots,|z|<1\) that satisfy the condition \({\partial\over\partial\theta} (\arg f'(re^{i\theta}))\geq \alpha\), \(0\leq\alpha< 1\), \(|z|= r\). Sufficient conditions (under some restrictions also necessary) are given and certain extremal questions are answered.

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