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A companion of Dragomir’s generalization of the Ostrowski inequality and applications to numerical integration

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Ukrainian Mathematical Journal Aims and scope

Some analogs of Dragomir’s generalization of the Ostrowski integral inequality

$$ \left| {\left( {b - a\left[ {\lambda \frac{{f(a) + f(b)}}{2} + \left( {1 - \lambda } \right)f(x)} \right] - \int\limits_a^b {f(t)dt} } \right)} \right| \leqslant \left[ {\frac{{{{\left( {b - a} \right)}^2}}}{4}\left( {\lambda^2 + {{\left( {1 - \lambda } \right)}^2}} \right) + {{\left( {x - \frac{{a + b}}{2}} \right)}^2}} \right]{\left\| {f'} \right\|_\infty } $$

are established. Some sharp inequalities are proved. An application to the composite quadrature rule is provided.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 4, pp. 435–450, April, 2012.

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Alomari, M.W. A companion of Dragomir’s generalization of the Ostrowski inequality and applications to numerical integration. Ukr Math J 64, 491–510 (2012). https://doi.org/10.1007/s11253-012-0661-x

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  • DOI: https://doi.org/10.1007/s11253-012-0661-x

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