Strong approximation of the solutions of a system of operator equations in Hilbert spaces
George L. Karakostas · The Journal of Difference Equations and Applications · 2006
We give sharp conditions for the strong approximation of the solutions of a system of the form by the solutions of a system of difference equations of the form where F i are monotone operators in a Hilbert space and is the metric projection. Thus, the results complete (and correct) those by Chidume et al. [Chidume, C.E. and Zegeye, H., 2004, Approximation of solutions of nonlinear equations of Hammerstein type in Hilbert spaces, Proceedings of the American Mathematical Society, 133(3), 851–858]. Also, we are interested in what happens when small perturbations of F i and q ij occur. Meanwhile, we generalize a numerical difference inequality due to Alber (see, e.g. Alber, Ya. I., 1983, Recurrence relations and variational inequalities, Soviet Mathematics Doklady, 27, 511–517) which is used to obtain approximation results.