We apply the method of linear interpolation of Kurchatov to solve nonlinear operator equations in Banach spaces. Using the principle of majorants of L. V. Kantorovich, we study the semilocal convergence of method of Kurchatov. Quadratic order of convergence of this method is determined. A priori and a posteriori estimations of method's error are received. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we present a two-step solver for nonlinear equations with a nondifferentiable operator. This method is based on two methods of order of convergence $1+\sqrt{2}$ . We study the local and a semilocal convergence using weaker conditions in order to extend the applicability of the solver. Finally, we present the numerical example that confirms the theoretical results.

In this work we introduce for the first time the generalized Lipschitz conditions for the divided difference operator. A positive integrable function, partial case of which is usual Lipschitz constant, is suggested. Under the given conditions the convergence of the Secant method for solving the operator equations in Banach spaces is investigated, the uniqueness ball for the solution is obtained. As a partial case the known results for the Lipschitz constants are received. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)