Convergence domains of certain iterative methods for solving nonlinear equations

Abstract

In this paper, we consider the iteration for solving the equation where f and g are operators in Banach spaces, f is Féchet differentiable, and A(x) is an approximation for f'(x), while the differentiability of g is not assumed. Under Zabrejko-Nguen type hypotheses, we determine a domain Ω such that starting from any point of Ω the method converges to a solution of the equation