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Estimation type results related to Fejér inequality with applications
M Rostamian Delavar1, S S Dragomir2, M De La Sen3
11Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran.
Journal of Inequalities and Applications
|April 21, 2018
Summary
This study introduces new bounds for Fejér type integral inequalities, refining estimates for the difference between integral parts. Applications include higher moments and trapezoidal error estimation.
Area of Science:
- Mathematical Analysis
- Inequalities Theory
Background:
- Fejér's integral inequality is a fundamental result in mathematical analysis.
- Existing inequalities provide bounds but can be refined for specific applications.
Purpose of the Study:
- To establish new theorems and inequalities for Fejér type integral inequalities.
- To provide tighter bounds for the difference between the right and middle parts of Fejér's inequality.
- To explore applications of these new inequalities.
Main Methods:
- Development of novel mathematical theorems and inequalities.
- Analytical techniques to derive new bounds for integral inequalities.
- Application of derived inequalities to specific mathematical problems.
Main Results:
- New theorems and inequalities related to Fejér type integral inequalities are presented.
- Improved bounds for the difference between integral parts are established.
- Demonstrated applicability to higher moments, trapezoidal error estimation, and special means.
Conclusions:
- The new inequalities offer enhanced estimations within the framework of Fejér's inequality.
- The findings contribute to the theory of integral inequalities and their applications.
- The study provides valuable tools for error estimation and analysis in probability and numerical methods.
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