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Coefficient inequalities for a subclass of Bazilevič functions

Sa’adatul Fitri, (Marjono), Derek Thomas, Ratno Bagus Edy Wibowo

Demonstratio Mathematica, Volume: 53, Issue: 1, Pages: 27 - 37

Swansea University Author: Derek Thomas

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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...

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Published in: Demonstratio Mathematica
ISSN: 2391-4661
Published: Walter de Gruyter GmbH 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa57027
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spelling 2021-07-08T13:09:29.8516836 v2 57027 2021-06-04 Coefficient inequalities for a subclass of Bazilevič functions 0e4f145bc8252e32a2293d49084a1fa5 Derek Thomas Derek Thomas true false 2021-06-04 FGSEN 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 &lt; 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 &lt; 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. Journal Article Demonstratio Mathematica 53 1 27 37 Walter de Gruyter GmbH 2391-4661 univalent functions, Bazilevi, coefficients, inverse, Fekete–Szegö, Hankel determinant 7 5 2020 2020-05-07 10.1515/dema-2020-0040 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-07-08T13:09:29.8516836 2021-06-04T09:48:48.0765353 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Sa’adatul Fitri 1 (Marjono) 2 Derek Thomas 3 Ratno Bagus Edy Wibowo 4 57027__20364__19844ac5e00a48f3b915bb882b34cb95.pdf 57027.pdf 2021-07-08T13:07:36.5653627 Output 1253026 application/pdf Version of Record true © 2020 Sa’adatul Fitri et al. This work is licensed under the Creative Commons Attribution 4.0 Public License true eng https://creativecommons.org/licenses/by/4.0/
title Coefficient inequalities for a subclass of Bazilevič functions
spellingShingle Coefficient inequalities for a subclass of Bazilevič functions
Derek Thomas
title_short Coefficient inequalities for a subclass of Bazilevič functions
title_full Coefficient inequalities for a subclass of Bazilevič functions
title_fullStr Coefficient inequalities for a subclass of Bazilevič functions
title_full_unstemmed Coefficient inequalities for a subclass of Bazilevič functions
title_sort Coefficient inequalities for a subclass of Bazilevič functions
author_id_str_mv 0e4f145bc8252e32a2293d49084a1fa5
author_id_fullname_str_mv 0e4f145bc8252e32a2293d49084a1fa5_***_Derek Thomas
author Derek Thomas
author2 Sa’adatul Fitri
(Marjono)
Derek Thomas
Ratno Bagus Edy Wibowo
format Journal article
container_title Demonstratio Mathematica
container_volume 53
container_issue 1
container_start_page 27
publishDate 2020
institution Swansea University
issn 2391-4661
doi_str_mv 10.1515/dema-2020-0040
publisher Walter de Gruyter GmbH
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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 &lt; 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 &lt; 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.
published_date 2020-05-07T04:12:27Z
_version_ 1763753849818972160
score 11.012678

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