Approximation Methods for Nonlinear Operator-Equations of the m-Accretive Type

Let E be a real Banach space which is both uniformly convex and uniformly smooth. Let T: D(T) ⊂ E → E be m-accretive, where the domain of T, D(T), is a proper subset of E. For any ƒ ∈ E, approximation methods are constructed which converge strongly to a solution of the operator equation x + Tx = ƒ. Explicit error estimates are obtained. A related result deals with operator equations of the dissipative type.