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

Merkle, Milan

Publ. Elektroteh. Fak., Univ. Beogr., Ser. Mat. 10, 113-117 (1999).

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.

Reviewer: Vesna Jevremović (Beograd)

MSC:

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

Keywords:

Ostrowski inequality; double-sided Ostrowski inequality; Hadamard inequality; distribution function