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 - <p style="text-align: justify;">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.</p>