Expanding the applicability of two-point Newton-like methods under generalized conditions
Ioannis K. Argyros, Saïd Hilout (2013)
Applicationes Mathematicae
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We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria...