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

DOI:
https://doi.org/10.1090/S0002-9939-07-08861-2

Published electronically:
June 20, 2007

MathSciNet review:
2322761

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-07-08861-2

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.