Fixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces

✍ Scribed by Somyot Plubtieng; Rattanaporn Punpaeng

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 236 KB
• Volume: 48
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/j.mcm.2007.10.002

✦ Synopsis

Let C be a nonempty closed convex subset of real Hilbert space H and S = {T (s) : 0 ≤ s < ∞} be a nonexpansive semigroup on C such that F(S) = ∅. For a contraction f on C, and t ∈ (0, 1), let x t ∈ C be the unique fixed point of the contraction

where {λ t } is a positive real divergent net. Consider also the iteration process {x n }, where x 0 ∈ C is arbitrary and

x n ds for n ≥ 0, where {α n }, {β n } ⊂ (0, 1) with α n + β n < 1 and {s n } are positive real divergent sequences. It is proved that {x t } and, under certain appropriate conditions on {α n } and {β n }, {x n } converges strongly to a common fixed point of S.