New conditions for the convergence of Newton-like methods and applications

Newton-like method methods are often used for solving nonlinear equations in a Banach space setting. Using more precise majorizing sequences, we provide a tighter convergence analysis than in earlier studies such as [4], [6], [9], [13], [17], [18], [19], [20], [21], [22], [31], [32], [33], [34], [35], [38], [39], [40], [41], [42], [43] and [44]. Our results are illustrated by several numerical examples, for which older convergence conditions do not hold but for which our convergence criteria are satisfied.