RESUMEN
Let X = Lp
(or 2p), 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.