|
Smale's mean value conjecture and the coefficients of univalent functions
Author(s):
Anthony
Conte;
Ege
Fujikawa;
Nikola
Lakic
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3295-3300.
MSC (2000):
Primary 30C10;
Secondary 30C50
Posted:
June 20, 2007
Retrieve article in:
PDF
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.
References:
-
- 1.
- Beardon, A. F., Minda, D. and Ng, T. W., Smale's mean value conjecture and the hyperbolic metric, Math. Ann. 322 (2002), 623-632. MR 1905109 (2003d:30005)
- 2.
- Crane, E. T., Extremal polynomials in Smale's mean value conjecture, Comput. Methods Funct. Theory. 6 (2006), 145-163. MR 2241037
- 3.
- Crane, E. T., A computational proof of the degree
 case of Smale's mean value conjecture, preprint. - 4.
- Duren, P., Univalent functions, Springer-Verlag, 1983. MR 708494 (85j:30034)
- 5.
- Henrici, P. and Kenan, W. R., Applied and Computational Complex Analysis, Vol. 3. Wiley, 1994. MR 822470 (87h:30002)
- 6.
- Ng, T. W., Smale's mean value conjecture for odd polynomials, J. Aust. Math. Soc. 75 (2003), 409-411. MR 2015325 (2004j:30013)
- 7.
- Shub, M. and Smale, S., Computational complexity: On the geometry of polynomials and the theory of cost. II, SIAM J. Comput. 15 (1986), 145-161. MR 822199 (87m:68044)
- 8.
- Smale, S., The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. (N. S.) 4 (1981), 1-36. MR 590817 (83i:65044)
- 9.
- Smale, S., Mathematical Problems for the Next Century, Mathematics: frontiers and perspectives, eds. Arnold, V., Atiyah, M., Lax, P. and Mazur, B., Amer. Math. Soc., 2000. MR 1754783 (2001i:00003)
- 10.
- Tischler, D., Perturbations of critical fixed points of analytic maps, Complex analytic methods in dynamical systems (Rio de Janeiro, 1992) Astérisque 222 (1994), 407-422. MR 1285398 (95k:30003)
- 11.
- Sheil-Small, T., Complex polynomials, Cambridge Studies in Advanced Mathematics 75, Cambridge, 2002. MR 1962935 (2004b:30001)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
30C10,
30C50
Retrieve articles in all Journals with MSC
(2000):
30C10,
30C50
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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org