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On the difference of inverse coefficients of convex functions
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...
| Published in: | The Journal of Analysis |
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| ISSN: | 0971-3611 2367-2501 |
| Published: |
Springer Science and Business Media LLC
2022
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa59145 |
| 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 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. |
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| Keywords: |
Difference of coefficients; Convex functions |
| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
875 |
| End Page: |
893 |