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.


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