Author's Personal Copy Computers and Mathematics with Applications a New Way to Think about Ostrowski-like Type Inequalities
Author's Personal Copy Computers and Mathematics with Applications a New Way to Think about Ostrowski-like Type Inequalities
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通讯作者：
V. N. Huy;Qú Ôc-Anh Ngô
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作者：
V. N. Huy;Qú Ôc-Anh Ngô
在大多数情况下，作者被允许将他们的文章版本（例如以Word或Tex形式）发布到他们的个人网站或机构存储库。作者需要进一步的信息，关于爱思唯尔的存档和手稿政策，鼓励访问：a B s t r a c t在这篇文章中，通过考虑一些已知的Ostrowski型不等式，我们提出了一种新的方法来处理一类Ostrowski型不等式涉及n点和m阶导数。精确地说，下面的不等式1 B − a B a f（x）dx − B − a n n i=1 f（a + xi（B − a））2 m + 5 4（B − a）m+1（m + 1）！（S − s）（）成立，其中S：= sup axb f（m）（m）（x），且对于适当的x 1，x 2，. ..，× n。值得注意的是，n，m是任意数。这意味着当m足够大时，（（）中的估计更准确。我们的方法也是基本的。
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t 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 1 b − a b a f (x) dx − b − a n n i=1 f (a + x i (b − a)) 2m + 5 4 (b − a) m+1 (m + 1)! (S − s) () holds, where S := sup axb f (m) (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.