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Smale's mean value conjecture for odd polynomials

Part of: Geometric function theory Riemann surfaces

Published online by Cambridge University Press:  09 April 2009

T. W. Ng
T. W. Ng
Affiliation:
Room 408, Run Run Shaw Building, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, e-mail: ntw@maths.hku.hk
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Abstract

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In this paper, we shall show that the constant in Smale's mean value theorem can be reduced to two for a large class of polynomials which includes the odd polynomials with nonzero linear term.

Keywords

Smale's mean value conjectureunivalent functionsomitted values

MSC classification

Secondary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 3 , December 2003 , pp. 409 - 412
Copyright
Copyright © Australian Mathematical Society 2003

References

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