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 C be a closed convex subset of a Hilbert space H H . Let { T ( t ) : t ≥ 0 } \{ T(t) : t ≥ 0 \} be a strongly continuous semigroup of nonexpansive mappings on C C such that ⋂ t ≥ 0 F ( T ( t ) ) ≠ ∅ t ≥ 0 F (T(t) ) ≠ ∅ . Let { α n } \{ α _n \} and { t n } \{ t_n \} be sequences of real numbers satisfying 0 > α n > 1 0 > α _n > 1 , t n > 0 t_n > 0 and lim n t n =