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 greater than or equal to 0} be a strongly continuous semigroup of nonexpansive mappings on C such that boolean AND(tgreater than or equal to0) F T(t)) not equal empty set. Let {alpha(n)} and {t(n)} be sequences of real numbers satisfying 0 < α(n) < 1, t(n) > 0 and lim(n) t(n) = lim(n) alpha(n)/t(n) = 0. Fix u is an element of C and define a sequence {u(n)} in C by u(n) = (1 - alpha(n)) T(t(n)) u(n) + alpha(n)u for n is an element of N. Then {u(n)} converges strongly to the element of boolean AND(tgreater than or equal to0) F T(t)) nearest to u.