Viscosity Approximation to Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces

Let C be a closed convex subset of a Hilbert space H , let {T (t) : t ≥ 0}be a strongly continuous semigroup of non-expansive mapping on C such that ⋂ t≥0 F (T (t)) = ∅, and f : C → C be a fixed contractive mapping. Let {αn} and {tn} be sequences of real numbers satisfying 0 < αn < 1, tn > 0 and limn tn = limn αn tn = 0. Define a sequence {xn} in C by xn = αnf(xn) + (1 − αn)T (tn)xn, for n ∈ N. Then {xn} converges strongly to the element of ⋂ t≥0 F (T (t)). Our results extent and improve corresponding ones of Tomonari Suzuki [Proc. Amer. Math. Soc., 131 (2002), 2133-2136] and Rudong Chen and Yunyan Song, Computers and Mathematics with Applications (Available online via http://www.sciencedirect.com/science/journal/03770427)