Sufficient conditions for bounded turning of analytic functions. (English) Zbl 1419.30009
Ukr. Math. J. 70, No. 8, 1288-1299 (2019); and Ukr. Mat. Zh. 70, No. 8, 1118-1127 (2018).
Summary: Consider a function \(f\) analytic in the open unit disk and normalized so that \(f(0) = f^\prime(0) - 1 = 0\). The methods of the theory of first-order differential subordinations are used to obtain sufficient conditions for the function \(f\) to have bounded turning, i.e., for the real part of its first derivative to map the unit disk onto the right half plane. In addition, several open problems are posed.
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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