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

Authors : İoannis K ARGYROS, Santhosh GEORGE

Pages : 137-144

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Publication Date : 2018-12-25

Article Type : Research Paper

Abstract :We present new sufficient convergence conditions for a two step Newton method insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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