Weak Semilocal Convergence Conditions for a Two-Step Newton Method in Banach Space

We present new sufficient convergence conditions for a two step Newton method (TSNM) to solve nonlinear equations in a Banach space setting. The new conditions depend on the center-Lipschitz constant instead of the Lipschitz constant. This way the applicability of (TSNM) is expanded in cases not covered before. Numerical examples are also provided in this study.

Keywords:

Newton's method, Modified Newton's method, Two step Newton method, Banach space, Lipschitz Semilocal convergence, center-Lipschitz condition,

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