On semilocal convergence analysis for two-step Newton method under generalized Lipschitz conditions in Banach spaces

In the present paper, we consider semilocal convergence issue of two-step Newton method for solving nonlinear operator equation in Banach spaces. Under assumption that first derivative satisfies a generalized Lipschitz condition, new analysis is presented. The Q-cubic obtained by an additional condition. This also allows us to obtain three important spacial cases about results based on premises Kantorovich, Smale and Nesterov-Nemirovskii types. As applications our results, nonsymmetric algebraic Riccati arising from transport theory two-dimensional convection-diffusion are provided.