Convergence theorems for semigroup of asymptotically nonexpansive mappings
نویسندگان
چکیده
In this paper, we prove the following results: Let K be a closed convex subset of a real Banach space E. Let T := {T (t) | t ∈ R+} be strongly continuous semigroup of asymptotically nonexpansive mappings from K into K such that F (T ) := ∩t∈R+F (T (t)) 6= ∅, where F (T (t)) = {x ∈ K |T (t)x = x} and R+ denotes the set of nonnegative real numbers. Then for arbitrary x0 ∈ K, the implicit iteration {xn} given by xn = αnxn−1 + (1 − αn) (T (tn)) xn , n ≥ 0 converges weakly (strongly) to an element of F (T ), where {αn}, {tn} are sequences of real numbers satisfying certain conditions.
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