Approximations and generalized Newton methods

We study local convergence of generalized Newton methods for both equations and inclusions by using known and new approximations and regularity properties at the solution. Including Kantorovich-type settings, our goal are statements about all (not only some) Newton sequences with appropriate initial points. Our basic tools are results of [31], [37] and [40], mainly about Newton maps and modified successive approximation, but also graph-approximations of multifunctions and others. Typical examples and simplifications of existing methods are added.