On the difference of inverse coefficients of convex functions

Sim, Young Jae; Thomas, Derek

doi:10.1007/s41478-021-00374-x

Journal article 114 views 72 downloads

On the difference of inverse coefficients of convex functions

Young Jae Sim, Derek Thomas

The Journal of Analysis, Volume: 30, Issue: 2, Pages: 875 - 893

Swansea University Author: Derek Thomas

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DOI (Published version): 10.1007/s41478-021-00374-x

Abstract

Let f be analytic in the unit disk D={z∈C:|z|<1}, and S be the subclass of normalised univalent functions given by f(z)=z+∑∞n=2anzn for z∈D. Let F be the inverse function of f defined in some set |ω|≤r0(f), and be given by F(ω)=ω+∑∞n=2Anωn. We prove the sharp inequalities −1/3≤|A4|−|A3|≤1/4 for t...

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Published in:	The Journal of Analysis
ISSN:	0971-3611 2367-2501
Published:	Springer Science and Business Media LLC 2022
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa59145
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first_indexed	2022-01-10T16:50:10Z
last_indexed	2022-06-16T03:19:29Z
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spelling	2022-06-15T14:54:08.4452704 v2 59145 2022-01-10 On the difference of inverse coefficients of convex functions 0e4f145bc8252e32a2293d49084a1fa5 Derek Thomas Derek Thomas true false 2022-01-10 FGSEN Let f be analytic in the unit disk D={z∈C:\|z\|<1}, and S be the subclass of normalised univalent functions given by f(z)=z+∑∞n=2anzn for z∈D. Let F be the inverse function of f defined in some set \|ω\|≤r0(f), and be given by F(ω)=ω+∑∞n=2Anωn. We prove the sharp inequalities −1/3≤\|A4\|−\|A3\|≤1/4 for the class K⊂S of convex functions, thus providing an analogue to the known sharp inequalities −1/3≤\|a4\|−\|a3\|≤1/4, and giving another example of an invariance property amongst coefficient functionals of convex functions. Journal Article The Journal of Analysis 30 2 875 893 Springer Science and Business Media LLC 0971-3611 2367-2501 Difference of coefficients; Convex functions 1 6 2022 2022-06-01 10.1007/s41478-021-00374-x http://dx.doi.org/10.1007/s41478-021-00374-x COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University SU Library paid the OA fee (TA Institutional Deal) 2022-06-15T14:54:08.4452704 2022-01-10T16:48:14.1394873 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Young Jae Sim 1 Derek Thomas 2 59145__22106__c9310c0f472e4f1f81ecc1abed00b742.pdf 59145.pdf 2022-01-10T16:50:37.3869988 Output 314750 application/pdf Version of Record true Copyright: Crown 2021. This article is licensed under a Creative Commons Attribution 4.0 International License true eng http://creativecommons.org/licenses/by/4.0/
title	On the difference of inverse coefficients of convex functions
spellingShingle	On the difference of inverse coefficients of convex functions Derek Thomas
title_short	On the difference of inverse coefficients of convex functions
title_full	On the difference of inverse coefficients of convex functions
title_fullStr	On the difference of inverse coefficients of convex functions
title_full_unstemmed	On the difference of inverse coefficients of convex functions
title_sort	On the difference of inverse coefficients of convex functions
author_id_str_mv	0e4f145bc8252e32a2293d49084a1fa5
author_id_fullname_str_mv	0e4f145bc8252e32a2293d49084a1fa5_***_Derek Thomas
author	Derek Thomas
author2	Young Jae Sim Derek Thomas
format	Journal article
container_title	The Journal of Analysis
container_volume	30
container_issue	2
container_start_page	875
publishDate	2022
institution	Swansea University
issn	0971-3611 2367-2501
doi_str_mv	10.1007/s41478-021-00374-x
publisher	Springer Science and Business Media LLC
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
url	http://dx.doi.org/10.1007/s41478-021-00374-x
document_store_str	1
active_str	0
description	Let f be analytic in the unit disk D={z∈C:\|z\|<1}, and S be the subclass of normalised univalent functions given by f(z)=z+∑∞n=2anzn for z∈D. Let F be the inverse function of f defined in some set \|ω\|≤r0(f), and be given by F(ω)=ω+∑∞n=2Anωn. We prove the sharp inequalities −1/3≤\|A4\|−\|A3\|≤1/4 for the class K⊂S of convex functions, thus providing an analogue to the known sharp inequalities −1/3≤\|a4\|−\|a3\|≤1/4, and giving another example of an invariance property amongst coefficient functionals of convex functions.
published_date	2022-06-01T04:16:13Z
_version_	1763754087510179840
score	11.012678

On the difference of inverse coefficients of convex functions

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