(untitled) (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 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.