A general iterative algorithm for nonexpansive mappings in Hilbert spaces |
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Authors: | Ming Tian |
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Affiliation: | College of Science, Civil Aviation University of China, Tianjin 300300, PR China |
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Abstract: | 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 F:H→H is a k-Lipschitzian and η-strongly monotone operator with k>0,η>0. Let . We proved that the sequence {xn} generated by the iterative method xn+1=αnγf(xn)+(I−μαnF)Txn converges strongly to a fixed point , which solves the variational inequality , for x∈Fix(T). |
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Keywords: | 47H09 47H05 47H06 47J25 47J05 |
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