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.
Authors
Ştefan M. Şoltuz
Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
Ishikawa-Mann iteration; associated Mann sequence
Paper coordinates
Ş.M. Şoltuz, On the boundedness of the associated sequence of Mann iteration for several operator classes with applications, Rev. Anal. Numer. Theor. Approx., 34 (2005) no. 2, 227-232, https://doi.org/10.33993/jnaat342-808
About this paper
Journal
Journal of Numerical Analysis and Approximation Theory
Publisher Name
Romanian Academy
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
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