The convergence domain for both the local and semilocal case of Newton’s method for Banach space valued operators is small in general. There is a plethora of articles that have extended the convergence criterion due to Kantorovich under variations of the convergence conditions. In this article, we use a different approach than before to increase the convergence domain, and without necessarily using conditions on the inverse of the Fréchet-derivative of the operator involved. Favorable to us applications are given to test the convergence criteria.