A new way to think about Ostrowski-like type inequalities

作者：Huy Vu Nhat; Ngo Quoc Anh^*

来源：Computers & Mathematics with Applications, 2010, 59(9): 3045-3052.

DOI：10.1016/j.camwa.2010.02.024

• Inequality
• Error
• Integral
• Taylor
• Ostrowski
• New estimations
• Numerical integration

In this present paper, by considering some known inequalities of Ostrowski-like type, we propose a new way to treat a class of Ostrowski-like type inequalities involving n points and m-th derivative. To be precise, the following inequality
vertical bar 1/b-a integral(b)(a)f(x) dx - b-a/n Sigma(n)(i=1)f (a + x(i)(b - a))vertical bar <= 2m + 5/4 (b - a)(m+1)/(m + 1)! (S - s) (*)
holds, where S := sup(a <= x <= b)f((m))(x), s := inf(a <= x <= b)f((m))(x) and for suitable x(1), x(2), ... , x(n) It is worth noticing that n, m are arbitrary numbers. This means that the estimate in (*) is more accurate when m is large enough. Our approach is also elementary.

• 出版日期2010-5