A companion of Dragomir’s generalization of the Ostrowski inequality and applications to numerical integration. (English. Russian original) Zbl 1257.26016

Alomari, M. W.

Ukr. Math. J. 64, No. 4, 491-510 (2012); translation from Ukr. Mat. Zh. 64, No. 4, 435-450 (2012).

Summary: Some analogs of Dragomir’s generalization of the Ostrowski integral inequality \[ \begin{split} \bigg| (b-a)\bigg[\lambda\frac{f(a)+f(b)}{2}+(1-\lambda)f(x)\bigg]-\int^b_af(t)dt\bigg| \\ \leq \bigg[\frac{(b-a)^2}{4}(\lambda^2+(1-\lambda)^2)+(x-\frac{a+b}{2})^2\bigg]\|f'\|_\infty \end{split} \] are established. Some sharp inequalities are proved. An application to the composite quadrature rule is provided.

MSC:

26D15

Inequalities for sums, series and integrals

Keywords:

generalization of the Ostrowski integral inequality; composite quadrature rule

References:

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