ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE-OPERATORS

Let E be a real Banach space with a uniformly convex dual. Suppose T: E --> E is a strongly accretive map with bounded range such that for each f is an element of E the equation Tx = f has a solution in E. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods), under suitable conditions, converges strongly to a solution of the equation Tx = f. Furthermore, our method shows that such a solution is necessarily unique. Explicit error estimates are given. Our results resolve in the affirmative an open problem (J. Math, Anal, Appl. 151, No. 2 (1990), 460) and generalize important known results. (C) 1995 Academic Press, Inc.