Let \(F, K: X \rightarrow X\) be accretive maps with \(D(K) = F(X) = X\) on a \(q\)-uniformly smooth, real Banach space \(X\). Under various continuity assumptions on \(F\) and \(K\) such that (1) \(0 = u + KFu\) has a solution, the authors consider iterative methods which converge strongly to a solution of (1) without requiring that \(K\) is invertible or that \(K\) and \(F\) are defined on compact subsets of \(X\). The proofs provide explicit algorithms for computing the solution of (1).