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Smale's mean value conjecture and the coefficients of univalent functions

Authors: Anthony Conte, Ege Fujikawa and Nikola Lakic
Journal: Proc. Amer. Math. Soc. 135 (2007), 3295-3300
MSC (2000): Primary 30C10; Secondary 30C50
Published electronically: June 20, 2007
MathSciNet review: 2322761
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Abstract: We study Smale's mean value conjecture and its connection with the second coefficients of univalent functions. We improve the bound on Smale's constant given by Beardon, Minda and Ng.

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Additional Information

Anthony Conte
Affiliation: Department of Mathematics, Graduate Center, CUNY, New York, New York 10016

Ege Fujikawa
Affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo, 152-8552 Japan
Address at time of publication: Department of Mathematics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554 Japan

Nikola Lakic
Affiliation: Department of Mathematics and Computer Science, Herbert H. Lehman College, CUNY, Bronx, New York 10468

Keywords: Polynomial, critical point, univalent function
Received by editor(s): June 2, 2005
Received by editor(s) in revised form: July 18, 2006
Published electronically: June 20, 2007
Additional Notes: The third author was partially supported by the grant DMS 0200733 from the National Science Foundation
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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