RESUMEN

Let X = L_p (or 2_p), p ≥ 2. The solution of the equation Ax = f, f є X is approximated in X by an iteration process in each of the following two cases: (i) A is bounded linear mapping of X into itself which is also bounded below; and (ii) A is nonlinear Lipschitz mapping of X into itself and satisfies < Ax – Ay, j(x-y) > ≥ m ║x-y║², for some constant m > 0 and for all x,y in X, where j is the single-valued normalized duality mapping of X into X^* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X.