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Generalized Ostrowski–Grüss-type Inequalities

Results in Mathematics, 2012
In this paper several inequalities of the following type are proved. Let \( c\geq 0\) and \(u_{c}(x):=c\left( x-\frac{a+b}{2}\right) .\) Then \[ \left| f(x)-\frac{1}{b-a}\int_{a}^{b}f(t)dt-\frac{f(b)-f(a)}{b-a} u_{c}(x)\right| \leq \left( 1+c\right) \widetilde{\omega }\left( f;\frac{ (x-a)^{2}+(b-x)^{2}}{2(b-a)}\right) \] for all \(f\in C[a,b]\) and ...
Gonska, Heiner   +2 more
openaire   +1 more source

On Multidimensional Ostrowski-Type Inequalities

Ukrainian Mathematical Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Multivariate Ostrowski Type Inequalities

Acta Mathematica Hungarica, 1997
The distance between the value \(f(x_{1},\cdots,x_{k})\) of a function \(f \in C^{1}(\prod^{k}_{i=1}[a_{i},b_{i}])\) and its integral mean can be estimated by the formula \[ \begin{gathered} \left| \frac{1}{\Pi^{k}_{i=1}(b_{i}-a_{i})} \int^{b_{1}}_{a_{1}}\int^{b_{2}}_{a_{2}} \cdots \int^{b_{k}}_{a_{k}} f(z_{1},\dots,z_{k})dz_{1}\ldots dz_{k} - f(x_{1},\
openaire   +2 more sources

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