论文信息 - On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces

On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces

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.

Tomonari Suzuki | Tomonari Suzuki

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