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Ostrowski type inequalities for sets and functions of bounded variation
1Department of Mechanics and Mathematics, O. Honchar Dnipro National University, pr. Gagarina, 72, Dnipro, 49010 Ukraine.
Journal of Inequalities and Applications
|July 7, 2017
Summary
This study presents sharp Ostrowski-type inequalities for multidimensional sets and multivariate functions with bounded variation. These findings advance integral inequality theory for complex mathematical spaces.
Area of Science:
- Mathematical Analysis
- Real Analysis
- Multivariate Calculus
Background:
- Ostrowski's inequality is a fundamental result in numerical integration and approximation theory.
- Generalizations of Ostrowski's inequality to higher dimensions and functions of bounded variation are crucial for advanced mathematical applications.
Purpose of the Study:
- To derive sharp Ostrowski-type inequalities.
- To extend these inequalities to multidimensional sets.
- To analyze these inequalities for multivariate functions of bounded variation.
Main Methods:
- Utilizing techniques from real analysis and measure theory.
- Applying concepts of total variation for multivariate functions.
- Developing novel approaches for multidimensional integration bounds.
Main Results:
- Obtained sharp error bounds for Ostrowski-type inequalities in multidimensional settings.
- Established new inequalities for functions exhibiting bounded variation in multiple dimensions.
- Demonstrated the sharpness of the derived inequalities.
Conclusions:
- The derived inequalities provide precise error estimates for multidimensional integration.
- These results contribute to the theoretical understanding of integral inequalities for complex function spaces.
- The findings have potential implications in numerical analysis and approximation theory.
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