On the boundedness of the associated sequence of Mann iteration for several operator classes with applications

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Ştefan M. Şoltuz

Abstract

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.

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Keywords
Ishikawa-Mann iteration; associated Mann sequence
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