2004 Conference on Diff. Eqns. and Appl. in Math. Biology, Nanaimo,
BC, Canada.
Electron. J. Diff. Eqns., Conference 12, 2005, pp. 7985.
Continuous Newton method for starlike functions
Yakov Lutsky
Abstract:
We study a continuous analogue of Newton method for
solving the nonlinear equation
where
holomorphic function and
.
It is proved that this method converges, to the solution for each initial
data
,
if and only if
is a starlike function with
respect to either an interior or a boundary point.
Our study is based on the theory of one parameter continuous semigroups.
It enables us to consider convergence in the case of an interior as
well as a boundary location of the solution by the same approach.
Published April 20, 2005.
Math Subject Classifications: 49M15, 46T25, 47H25.
Key Words: Newton method; starlike functions; continuous semigroup.
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Yakov Lutsky
Department of Mathematics
Ort Braude College
Karmiel 21982, Israel
email: yalutsky@yahoo.com

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