TY - JOUR
T1 - Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions
AU - Prakash Jaiswal , Jai
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 650
EP - 657
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.650
UR - https://global-sci.org/intro/article_detail/jnma/21903.html
KW - Banach space, Nonlinear equation, Lipschitz condition, $L$-average,
Convergence ball.
AB - <p style="text-align: justify;">In this paper, we study the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weaker
hypothesis. More precisely, we derive the existence and uniqueness theorems,
when the first-order derivative of nonlinear operator satisfies the $L$-average
conditions instead of the usual Lipschitz condition, which have been discussed
in the earlier study.</p>