STABLE ITERATION SCHEMES FOR LOCAL STRONGLY PSEUDOCONTRACTIONS AND NONLINEAR EQUATIONS INVOLVING LOCAL STRONGLY ACCRETIVE OPERATORS

Abstract. Let T be a local strongly pseudocontractive and uniformly con-tinuous operator from an arbitrary Banach space X into itself. Under certain conditions, we establish that the Noor iteration scheme with errors both con-verges strongly to a unique fixed point of T and is almost T-stable. The related results deal with the convergence and almost stability of the Noor iteration scheme with errors of solutions of nonlinear equations of the local strongly accretive type. 1