Forcing Strong Convergence of a Mann-Based Iteration for Nonexpansive and Monotone Operators in a Hilbert Space

Mann iteration is weakly convergent in infinite dimensional spaces. We, in this paper, use the nearest point projection to force the strong convergence of a Mann-based iteration for nonexpansive and monotone operators. A strong convergence theorem of common elements is obtained in an infinite dimens...

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Veröffentlicht in:Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
1. Verfasser: Lv, Songtao
Format: Artikel
Sprache:eng
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Zusammenfassung:Mann iteration is weakly convergent in infinite dimensional spaces. We, in this paper, use the nearest point projection to force the strong convergence of a Mann-based iteration for nonexpansive and monotone operators. A strong convergence theorem of common elements is obtained in an infinite dimensional Hilbert space. No compact conditions are needed.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/5450521