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On the logarithmic coefficients of close to convex functions


Author: D. K. Thomas
Journal: Proc. Amer. Math. Soc. 144 (2016), 1681-1687
MSC (2010): Primary 30C45; Secondary 30C50
DOI: https://doi.org/10.1090/proc/12921
Published electronically: September 24, 2015
MathSciNet review: 3451243
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Abstract: For $ f$ analytic and close to convex in $ D=\{z: \vert z\vert< 1\}$, we give sharp estimates for the logarithmic coefficients $ \gamma _{n}$ of $ f$ defined by $ \log \dfrac {f(z)}{z}=2\sum _{n=1}^{\infty } \gamma _{n}z^{n}$ when $ n=1, 2,3$.


References [Enhancements On Off] (What's this?)

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Additional Information

D. K. Thomas
Affiliation: Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom
Email: d.k.thomas@swansea.ac.uk

DOI: https://doi.org/10.1090/proc/12921
Keywords: Univalent functions, close to convex functions, logarithmic coefficients
Received by editor(s): January 15, 2015
Received by editor(s) in revised form: February 22, 2015, February 25, 2015, and May 14, 2015
Published electronically: September 24, 2015
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society

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