an implicit iteration process for nonexpansive semigroups

let c be a closed convex subset of a banach space e. let {t (t) : t ⩾ 0} be a strongly continuous semigroup of nonexpansive mappings on c such that ∩_t⩾0 f (t (t)) ̸= ∅. let {α_n} and {t_n} be sequences of real numbers satisfying appropriate conditions, then for arbitrary x₀ ∈ c, the mann type implicit iteration process {xn} given by x_n = α_nx_n−1 + (1 −α_n)t (t_n)x_n, n ⩾0, weakly (strongly) converges to an element of ∩_t⩾0f (t (t)).