Published online by Cambridge University Press: 17 February 2009
Conditions are given for a Ck map T to be a Newton map, that is, the map associated with a differentiable real-valued function via Newton's method. For finitely differentiable maps and functions, these conditions are only necessary, but in the smooth case, that is, for k = ∞, they are also sufficient. The characterisation rests upon the structure of the fixed point set of T and the value of the derivative T′ there, and it is best possible as is demonstrated through examples.