Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we study the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weakerhypothesis. More precisely, we derive the existence and uniqueness theorems,when the first-order derivative of nonlinear operator satisfies the $L$-averageconditions instead of the usual Lipschitz condition, which have been discussedin the earlier study.