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A general iterative algorithm for nonexpansive mappings in Hilbert spaces

✍ Scribed by Ming Tian

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 250 KB
Volume: 73
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.03.058

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✦ Synopsis

Let H be a real Hilbert space. Suppose that T is a nonexpansive mapping on H with a fixed point, f is a contraction on H with coefficient 0 < α < 1, and

2 )/α = τ /α. We proved that the sequence {x n } generated by the iterative method

)Tx n converges strongly to a fixed point x ∈ F ix (T ), which solves the variational inequality (γ f -µF )x, xx ≤ 0, for x ∈ F ix (T ).

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