Sharp bounds of Hankel determinant for the inverse functions on a subclass of bounded turning functions. (English) Zbl 1510.30004
Summary: The purpose of this paper is to determine the estimates of some coefficient-related problems for the class \(\mathcal{B}\mathcal{T}_{3\ell}\) of bounded turning functions connected to a three-leaf shaped domain. We calculate the upper bounds of the second and third order Hankel determinants with the coefficients of the inverse functions. The bounds are proved to be sharp.
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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