General Iterative Algorithm for Nonexpansive Semigroups and Variational Inequalities in Hilbert Spaces
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چکیده
Let H be a real Hilbert space with inner product 〈·, ·〉 and norm ‖ · ‖, respectively. Let C be a nonempty closed convex subset of H and let PC be the metric projection of H onto C. A mapping T of C into itself is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for each x, y ∈ C. We denote by F T the set of fixed points of T . A family S {T s : 0 ≤ s < ∞} of mappings of C into itself is called a nonexpansive semigroup on C if it satisfies the following conditions:
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