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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 iteratively by x0 ∈ K, xn+1 = (1 – Cn)xn + CnSxn, n ≥ 0, where is a real sequence satisfying appropriate conditions. Then, for any given f in K, the sequence 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.