ON THE BOUNDENESS OF THE ASSOCIATED SEQUENCE OF MANN ITERATION FOR SEVERAL OPERATOR CLASSES WITH APPLICATIONS *

S ¸tefan, M ¸oltuz
2005 Rev. Anal. Numér. Théor. Approx   unpublished
We prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfy 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. MSC 2000. 47H10.
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