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- W1990486501 abstract "Let H be a real Hilbert space.Suppose that T is a nonexpansive mapping on H with a fixed point, G is a L-Lipschitzian mapping on H with coefficient L > 0, and F : H → H is a k- Lipschitzian and η-strongly monotone operator with k > 0, η > O. Let 0 <; μ <; 2η/k <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> , 0 <; γ <; μ(η - μk <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> /2)/L = τ/L. We pointed out the relationship between Yamada's method and viscosity iteration and proved that the sequence {x <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>η</sub> } generated by the iterative method x <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>η+1</sub> = α <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> γG(x <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> ) + (I - μα <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> F)Tx <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> converges strongly to a fixed point x̃ ∈ F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>ix</sub> (T), which solves the variational inequality ((γG - μF)x̃, x-x̃) ≤ 0, for x ∈ F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>ix</sub> (T)." @default.
- W1990486501 created "2016-06-24" @default.
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- W1990486501 date "2010-12-01" @default.
- W1990486501 modified "2023-09-27" @default.
- W1990486501 title "A General Iterative Method Based on the Hybrid Steepest Descent Scheme for Nonexpansive Mappings in Hilbert Spaces" @default.
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- W1990486501 doi "https://doi.org/10.1109/cise.2010.5677064" @default.
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