On the boundedness of the associated sequence of Mann iteration for several operator classes with applications - Ştefan M. Şoltuz (Journal of Numerical Analysis and Approximation Theory, 2005)
We prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfies minimal assumptions. In particular we obtain for a nonexpansive operator that the associated sequence of Ishikawa iteration is decreasing for a nonexpansive operator. Applications to the convergence of Mann iteration are given.