ITERATIVE SOLUTION OF NONLINEAR EQUATIONS OF THE MONOTONE TYPE IN BANACH-SPACES

Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Suppose T: K → K is a continuous monotone map. Define S: K → K by Sx = f — Tx for each x in K and define the sequence [formula omitted] iteratively by x0 [formula omitted] K., xn+1 = (1 — Cn)xn + CnSxn, n ≥ 0, where [formula omitted] is a real sequence satisfying appropriate conditions. Then, for any given f in K., the sequence [formula omitted] converges strongly to a solution of x + Tx = f in K. Explicit error estimates are also computed. A related result deals with iterative solution of nonlinear equations of the dissipative type. © 1990, Australian Mathematical Society. All rights reserved.