Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations

Let H be a real Hilbert space, K a nonempty closed convex subset of H and T : K → K a Lipschitz pseudocontraction with a nonempty fixed-point set. Weak and strong convergence theorems for the iterative approximation of fixed points of T are proved. Furthermore, if T : H → H is a Lipschitz monotone operator and f R(T), where R(T) denotes the range of T, weak and strong convergence theorems for the iterative approximation of solutions of the operator equation Tx = f are proved.