A NEWTON-LIKE METHOD FOR SOLVING GENERALIZED OPERATOR EQUATIONS AND VARIATIONAL INEQUALITIES

In this paper, we present a semilocal convergence analysis of a Newton-like method for solving the generalized operator equations in Hilbert spaces and also discuss the convergence analysis of the proposed algorithm under weak conditions. We establish sharp generalizations of Kantorovich theory for operator equations when the derivative is not necessarily invertible. As a simple consequence of our result, we discuss the existence and uniqueness of solutions of mixed variational inequality problems. Finally, we give numerical examples for the equations involving single valued as well as multi-valued mappings.