{'fraction_non_alphanumeric': 0.008130081300813009, 'fraction_numerical': 0.0040650406504065045, 'mean_word_length': 4.6022727272727275, '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 of iterates and differentiability

Given a function T mapping a Hausdorff locally convex topological vector space Φ into Φ and a point φ0 of Φ, convergence of the elementary filter associated with the sequence of iterates determined by T and φ0 is investigated. Sufficient conditions that the limit φ if it exists, be a fixed point of T are given and in the case Φ is the space of real valued functions of a real variable differentiability of the limit function φ is investigated.