A companion of Dragomir's generalization of Ostrowski's inequality and applications in numerical integration

• Date: 2012
• Main Authors: Alomari, M. W., Аломарі, М. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2588
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

\lambda) f(x) - \int^b_a f(t)dt\right]\right| \leq$$ $$\leq\left[\frac{(b-a)^2}{4}(\lambda^2 + (1 - \lambda)^2) + \left(x - \frac{a + b}{2}\right)^2\right] ||f'||_{\infty}$$ are established. Some sharp inequalities are proved. An application to a composite quadrature rule is provided.