On the boundedness of the associated sequence of Mann iteration for several operator classes with applications
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. Applicat...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2005-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/808 |
| Summary: | 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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| ISSN: | 2457-6794 2501-059X |