{'fraction_non_alphanumeric': 0.05215419501133787, 'fraction_numerical': 0.0, 'mean_word_length': 4.1395348837209305, '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}}
A sharp companion of Ostrowski's inequality for the Riemann-Stieltjes integral and applications

A sharp companion of  Ostrowski's inequality for the Riemann-Stieltjes integral ∫ a b f ( t ) du ( t ), where f is assumed to be of r-H -Holder type on [ a,b ] and u is of bounded variation on [ a,b ], is proved. Applications to the approximation problem of the Riemann-Stieltjesintegral in terms of Riemann-Stieltjes sums are also pointed out.