On the Local Convergence of Two-Step Newton Type Method in Banach Spaces under Generalized Lipschitz Conditions

The motive of this paper is to discuss the local convergence a two-step Newton-type method rate three for solving nonlinear equations in Banach spaces. It assumed that first order derivative operator satisfies generalized Lipschitz i.e., L-average condition. Also, some results on same spaces are established under assumption operators radius or center condition with weak particularly it L positive integrable function but not necessarily non-decreasing. Our new idea gives tighter analysis without conditions. proposed technique useful expanding applicability iterative methods. Useful examples justify theoretical conclusions.