A General Iterative Method Based on the Hybrid Steepest Descent Scheme for Nonexpansive Mappings in Hilbert Spaces
Ming Tian · 2010
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 02, 02/2)/L = τ/L. We pointed out the relationship between Yamada's method and viscosity iteration and proved that the sequence {xη} generated by the iterative method xη+1= αnγG(xn) + (I - μαnF)Txnconverges strongly to a fixed point x̃ ∈ Fix(T), which solves the variational inequality ((γG - μF)x̃, x-x̃) ≤ 0, for x ∈ Fix(T).