{'fraction_non_alphanumeric': 0.10120845921450151, 'fraction_numerical': 0.0075528700906344415, 'mean_word_length': 3.9849624060150375, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Convergence theorems for semigroup of asymptotically nonexpansive mappings

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.