ON DOMINATING SEQUENCE METHOD IN THE POINT ESTIMATE AND SMALE THEOREM

It can be optimized for the work of the point estimate on the Newton iteration, reported by Smale at the 20th Congress of Mathematicians in 1986. It has been proved that iffα(z,f) , for every analytic map f:E→F, z ∈ is an approximate zero of f,whereE and F are real or complex Banach spaces. In addition, if α,(z,f) , z is anapproximate zero of the second kind of f.