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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: ajconte520@hotmail.com

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
Email: fujikawa@mm.sophia.ac.jp

Nikola Lakic
Affiliation: Department of Mathematics and Computer Science, Herbert H. Lehman College, CUNY, Bronx, New York 10468
Email: nikola.lakic@lehman.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08861-2
PII: S 0002-9939(07)08861-2
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.