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Some generalizations of Hermite-Hadamard type inequalities
M Rostamian Delavar1, M De La Sen2
1Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran.
Springerplus
|October 13, 2016
Summary
This study explores generalizations of Hermite-Hadamard inequalities for [Formula: see text]-convex functions. Applications to trapezoid and mid-point inequalities are also presented, advancing mathematical analysis.
Area of Science:
- Mathematical Analysis
- Convexity Theory
Background:
- The Hermite-Hadamard inequality is a fundamental result in classical analysis.
- Investigating generalizations of established inequalities provides deeper insights into mathematical structures.
- The concept of [Formula: see text]-convex functions extends classical convexity, offering new avenues for research.
Purpose of the Study:
- To generalize and refine Hermite-Hadamard type inequalities.
- To explore these inequalities in the context of [Formula: see text]-convex functions.
- To demonstrate the applicability of these refined inequalities to trapezoid and mid-point type inequalities.
Main Methods:
- Utilizing analytical techniques to derive new inequality bounds.
- Applying definitions and properties of [Formula: see text]-convex functions.
- Developing specific cases and applications for trapezoid and mid-point formulas.
Main Results:
- Established new generalizations and refinements of Hermite-Hadamard inequalities.
- Demonstrated the relationship between these inequalities and [Formula: see text]-convex functions.
- Provided novel applications for trapezoid and mid-point inequalities based on the derived results.
Conclusions:
- The study successfully extended Hermite-Hadamard inequalities to the domain of [Formula: see text]-convex functions.
- The findings offer valuable tools for further research in mathematical analysis and inequality theory.
- The applications highlight the practical relevance of these theoretical advancements.
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