On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings. (English) Zbl 1488.30132
Summary: In this paper, we obtain the upper bounds to the third Hankel determinants for convex functions of order \(\alpha\) and bounded turning functions of order \(\alpha\). Furthermore, several relevant results on a new subclass of close-to-convex harmonic mappings are obtained. Connections of the results presented here to those that can be found in the literature are also discussed.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 58E20 | Harmonic maps, etc. |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
Keywords:
univalent function; starlike function; convex function; bounded turning function; close-to-convex function; harmonic mapping; Hankel determinantReferences:
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