Estimates for analytic functions concerned with Hankel determinant
UDC 517.5 We give an upper bound of Hankel determinant of the first order $(H_{2}(1))$ for the classes of an analytic function. In addition, an evaluation with the Hankel determinant from below will be given for the second angular derivative of $f(z)$ analytic function. For new inequalities, the res...
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| Date: | 2021 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/907 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We give an upper bound of Hankel determinant of the first order $(H_{2}(1))$ for the classes of an analytic function. In addition, an evaluation with the Hankel determinant from below will be given for the second angular derivative of $f(z)$ analytic function. For new inequalities, the results of Jack's lemma and Hankel determinant were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of an angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.
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| DOI: | 10.37863/umzh.v73i9.907 |