| Abstract: | In a real or oompbx Banach space X, let P be an operator with Lipsohitzcontinnous Frechet derivative P', and [{X_*} in X] such that [P({X_*}) = 0] and [{P^'}{({X_*})^{ - 1}}] exists.It is shown that a ball with center [{X_*}] and best possible radius such that the theorem ofMysoyskich guarantees convergenee of Newton's method to [{X_*}] starting from any point[{x_0}] in ihe ball (theorem 3). In comparison with the corresponding results of Rall's workon Kantorovich theorem, the radius obtained is smaller than that from Kantorovichtheorem. Therefore we suggest here an improved form of Mysoyskich theorem (theorem1) . Thus, the corresponding value of the radius is augmented beyond that fromKantorovich theorem (theorem 2). |
