Abstract
In this paper, we prove the following strong convergence theorem: Let C be a closed convex subset of a Hilbert space H. Let {T(t) : t ≥ 0} be a strongly continuous semigroup of nonexpansive mappings on C such that ∩ t>0 F (T(t)) ¬= 0. Let {α n } and {t n } be sequences of real numbers satisfying 0 0 and lim n t n = lim n α n /t n = 0. Fix u E C and define a sequence {u n } in C by u n = (1 - α n )T(t n )u n + α n u for n E N. Then {u n } converges strongly to the element of ∩ t>0 F(T(t)) nearest to u.
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