Riemann-Stieltjes integrals and some Ostrowski type inequalities. (English) Zbl 1513.26024
Summary: In this article, we investigate new integral inequalities of Ostrowski’s type of various functional aspects. For mapping’s second derivative, we assume two cases, namely, \(L_1\) and \(L_\infty\) spaces. Moreover, for first derivative, we investigate two different characteristics, namely, bounded variation and locally Lipchitz continuity. Applications to special means and composite quadrature rules are also carried out.
MSC:
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
| 26A45 | Functions of bounded variation, generalizations |
| 26D15 | Inequalities for sums, series and integrals |
Keywords:
Ostrowski inequality; bounded variation; Riemann-Stieltjes integral; locally Lipschitz continuousReferences:
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