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Remarks on Ostrowski’s and Hadamard’s inequality. (English) Zbl 0946.26016

In this paper a general inequality is obtained starting from Taylor’s formula with an integral form of remainder. This inequality gives the Ostrowski’s and Hadamard’s inequality as special cases. Finally, the two-sided version of the Ostrowski’s inequality is given and applied in the probability theory as one possibility of estimating the tails of a distribution function concentrated on a finite interval.

MSC:

26D15 Inequalities for sums, series and integrals
60E15 Inequalities; stochastic orderings
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