Majorizing sequences for iterative methods

摘要

We provide convergence results for very general majorizing sequences of iterative methods. Using our new concept of recurrent functions, we unify the semilocal convergence analysis of Newton-type methods (NTM) under more general Lipschitz-type conditions. We present two very general majorizing sequences and we extend the applicability of (NTM) using the same information before Chen and Yamamoto (1989) [13], Deuflhard (2004) [16], Kantorovich and Akilov (1982) [19], Miel (1979) [20], Miel (1980) [21] and Rheinboldt (1968) [30]. Applications, special cases and examples are also provided in this study to justify the theoretical results of our new approach.