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Coefficient inequalities for a subclass of Bazilevič functions
Demonstratio Mathematica, Volume: 53, Issue: 1, Pages: 27 - 37
Swansea University Author: Derek Thomas
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© 2020 Sa’adatul Fitri et al. This work is licensed under the Creative Commons Attribution 4.0 Public License
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DOI (Published version): 10.1515/dema-2020-0040
Abstract
AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying \left|f^{\p...
| Published in: | Demonstratio Mathematica |
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| ISSN: | 2391-4661 |
| Published: |
Walter de Gruyter GmbH
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa57027 |
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| Abstract: |
AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying \left|f^{\prime} (z){\left(\frac{z}{f(z)}\right)}^{1-\alpha }-1\right|\lt \lambda for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f\in { {\mathcal B} }_{1}(\alpha ,\lambda ), thus extending recent work in the case λ = 1. |
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| Keywords: |
univalent functions, Bazilevi, coefficients, inverse, Fekete–Szegö, Hankel determinant |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
27 |
| End Page: |
37 |