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Jensen-Steffensen inequality for strongly convex functions
1Faculty of Science, University of Split, Split, Croatia.
Journal of Inequalities and Applications
|March 7, 2019
Summary
The Jensen-Steffensen inequality extends the standard Jensen inequality by allowing negative weights. This study proves this generalized inequality specifically for strongly convex functions, broadening its applicability in mathematical analysis.
Area of Science:
- Mathematical Analysis
- Convexity Theory
Background:
- The Jensen inequality is fundamental for convex functions with non-negative weights.
- The Jensen-Steffensen inequality generalizes Jensen's by permitting negative weights.
Purpose of the Study:
- To prove the Jensen-Steffensen inequality for strongly convex functions.
- To extend the applicability of generalized Jensen inequalities.
Main Methods:
- Utilizing properties of strongly convex functions.
- Applying techniques from mathematical analysis to inequalities.
Main Results:
- The Jensen-Steffensen inequality is established for strongly convex functions.
- Demonstration of the inequality under relaxed weight conditions.
Conclusions:
- The findings confirm the validity of the Jensen-Steffensen inequality for a significant class of functions.
- This work contributes to a deeper understanding of generalized inequalities in convex analysis.
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