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On a Mann type implicit iteration process for continuous pseudo-contractive mappings

✍ Scribed by Yisheng Song

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 190 KB
Volume: 67
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2006.09.059

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✦ Synopsis

Let K be a nonempty closed convex subset of a Banach space E, T : K → K a continuous pseudo-contractive mapping. Suppose that {α n } is a real sequence in [0, 1] satisfying appropriate conditions; then for arbitrary x 0 ∈ K , the Mann type implicit iteration process {x n } given by x n = α n x n-1 + (1 -α n )T x n , n ≥ 0, strongly and weakly converges to a fixed point of T , respectively.

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