- Volume 15 Issue 4
We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in . We also provide a comparative study between results using the classical Newton-Kantorovich conditions (, , ), and the ones using the gamma-type conditions (, ). Numerical examples are also provided.