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 Klatte-Kummer (2002) and Kummer (1988, 1995), 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.
Mathematical Programming Ser. B, accepted version. DOI 10.1007/s10107-017-1194-8 Published online 11 September 2017, the final version is available at link.springer.com