Hussain, Sabir; Qayyum, Ather A generalized Ostrowski-Grüss type inequality for bounded differentiable mappings and its applications. (English) Zbl 1282.26025 J. Inequal. Appl. 2013, Paper No. 1, 7 p. (2013). In 1938, A. Ostrowski obtained a bound for the approximation of a differentiable function by its integral average. If \(f\) is a differentiable real mapping on an interval \(I\), \(a,b\in I\) with \(a<b\) and \(|f'(t)|\leq M\) for all \(t\in[a,b]\), then the inequality \[ \left|f(x)-\frac{1}{b-a}\int_{a}^{b}f(t)dt\right|\leq\left[\frac{1}{4}+ \left(\frac{x-\frac{a+b}{2}}{b-a}\right)^2\right](b-a)M, \] known as the Ostrowski inequality, holds true for every \(x\in[a,b]\). The constant \(\frac{1}{4}\) is the best possible one. In this paper, the authors present some inequalities of Ostrowski type including some weight functions. Reviewer: Mohsen Kian (Bojnord) Cited in 25 Documents MSC: 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals Keywords:Ostrowski inequality; weight function; error bound PDFBibTeX XMLCite \textit{S. Hussain} and \textit{A. Qayyum}, J. Inequal. Appl. 2013, Paper No. 1, 7 p. (2013; Zbl 1282.26025) Full Text: DOI References: [1] doi:10.1016/j.aml.2012.02.052 · Zbl 1254.26034 · doi:10.1016/j.aml.2012.02.052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.