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

Authors : Ioannis K Argyros, Santhosh George

Pages : 137-144

View : 15 | Download : 9

Publication Date : 2018-12-25

Article Type : Research

Abstract :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