TY - JOUR T1 - Semilocal Convergence Theorem for a Newton-Like Method JO - East Asian Journal on Applied Mathematics VL - 3 SP - 482 EP - 494 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.090816.270317a UR - https://global-sci.org/intro/article_detail/eajam/10760.html KW - Newton-like method, nonlinear equation, Newton-Kantorovich theorem, γ-condition, error estimate. AB -
The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.