Strong Convergence Theorems of Halpern's Type for Families of Nonexpansive Mappings in Hilbert Spaces

Let C be a nonempty closed convex subset of a real Hilbert space and let {T-n} be a family of nonexpansive mappings of C into itself such that the set of all common fixed points of {Tn} is nonempty. We consider a sequence {x(n)} generated by x(1) = x is an element of C, = x(n) (vertical bar) (1) = alpha(n)x + (1 - alpha(n))T-n(beta(n)x + (1 - beta(n))x(n)) (for all(n) is an element of N), where {alpha(n)} subset of [0,1) and {beta(n)} subset of [0,1). Then, we give the conditions of {alpha(n)}, {beta(n)} and {T-n} under which {x(n)} converges strongly to a common fixed point of {T-n}.