Funktionalungleichungen und Iterationsverfahren

This paper is concerned with a class of iterative processes of the formu _k+1 =Tu _k (k = 0, 1, ?) for solving nonlinear operator equationsu = Tu orFu = 0. By studying the relationship between a linear functional inequality?(Ah) β(h) + γ(h) ? ?(h) and estimates for the iteration operatorT a general semilocal convergence theorem is obtained. The theorem contains as special cases theorems for various iterative methods. Numerical examples illustrate the accuracy of the error estimates for the approximationu _k .