On Strong Convergence to Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
نویسنده
چکیده
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) ) 6= ∅. Let {αn} and {tn} be sequences of real numbers satisfying 0 < αn < 1, tn > 0 and limn tn = limn αn/tn = 0. Fix u ∈ C and define a sequence {un} in C by un = (1 − αn)T (tn)un + αnu for n ∈ N. Then {un} converges strongly to the element of ⋂ t≥0 F ( T (t) ) nearest to u.
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