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A general iterative algorithm for nonexpansive mappings in Hilbert spaces

A general iterative algorithm for nonexpansive mappings in Hilbert spaces,10.1016/j.na.2010.03.058,Nonlinear Analysis-theory Methods & Applications,Mi

A general iterative algorithm for nonexpansive mappings in Hilbert spaces   (Citations: 7)
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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 0α1, and F:H→H is a k-Lipschitzian and η-strongly monotone operator with k>0,η>0. Let 0μ2η/k2,0γμ(η−μk22)/α=τ/α. We proved that the sequence {xn} generated by the iterative method xn+1=αnγf(xn)+(I−μαnF)Txn converges strongly to a fixed point x̃∈Fix(T), which solves the variational inequality 〈(γf−μF)x̃,x−x̃〉≤0, for x∈Fix(T).
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    • ...Very recently,M.Tian [9] proposed a general iterative method for Nonexpansive Mappings that contains algorithms defined by G.Marino,H.K.Xu and Yamada :...
    • ...where T is a self-nonexpansive mapping on H,F is k−Lipschitzian continuous and η−strongly monotone operator on H and f is a contraction on H.Then M.Tian[9] proved the sequence defined by above iterative process converges strongly to a fixed point of T...
    • ...Then we extend and generalize the iterative method introduced by Tian [9] and consider the following general iterative method...

    Ming Tian. A General Iterative Method Based on the Hybrid Steepest Descent Scheme...

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