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Weighted Ostrowski, Ostrowski-Gruss and Ostrowski--Cebysev type inequalities on time scales
Publicationes Mathematicae Debrecen, 2012Recently several authors have extended various classical inequalities to inequalities on time scales, an important concept due to Hilger that enables discrete and continuous results to be proved simultaneously, see in particular \textit{R. Agarwal, M. Bohner and A. Peterson} [Math. Inequal. Appl. 4, 535--557 (2001; Zbl 1021.34005)], \textit{M.
Tuna, Adnan, Jiang, Yong, Liu, Wenjun
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Generalized Ostrowski–Grüss-type Inequalities
Results in Mathematics, 2012In 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
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On Multidimensional Ostrowski-Type Inequalities
Ukrainian Mathematical Journal, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Univariate Ostrowski Inequalities, Revisited
Monatshefte f?r Mathematik, 2002The author proves several new identities of Montgomery-type (such an identity was used by Montgomery in multiplicative number theory); then certain general Ostrowski type inequalities, involving \(L_p\) (\(p\geq 1\), or \(p=\infty\)) are deduced. There are too many results (17 theorems and a couple of consequences), and too complicated to be stated ...
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On Ostrowski inequality for quantum calculus
Applied Mathematics and Computation, 2021We disprove a version of Ostrowski inequality for quantum calculus appearing in the literature. We derive a correct statement and prove that our new inequality is sharp. We also derive a midpoint inequality.
Aglić-Aljinović, Andrea +3 more
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Two-Point Ostrowski’s Inequality
Results in Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multivariate Ostrowski Type Inequalities
Acta Mathematica Hungarica, 1997The 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},\
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Some Weighted Ostrowski Type Inequalities
Vietnam Journal of Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized Ostrowski and Ostrowski-Grüss type inequalities
Rendiconti del Circolo Matematico di Palermo Series 2zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ghulam Farid +5 more
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2010
We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over \([a, b] \subset {\mathbb R}\), error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions.
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We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over \([a, b] \subset {\mathbb R}\), error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions.
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