On one estimate of divided differences and its applications

• Дата: 2019
• Автори: Kopotun, K. A., Leviatan, D., Shevchuk, I. A., Копотун, К. А., Левіатан, Д., Шевчук, І. О.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2019
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/1434
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We give an estimate of the general divided differences $[x_0, ..., x_m; f]$, where some points xi are allowed to coalesce (in this case, $f$ is assumed to be sufficiently smooth). This estimate is then applied to significantly strengthen the celebrated Whitney and Marchaud inequalities and their gen...