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Rev. Anal. Numér. Théor. Approx
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.fatcat:3ysux6v4rzfipglq45zmbpzzd4