An Extension of Steffensen's Inequality
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2026
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| _version_ | 1866901891730898944 |
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| author | Tuan, Tran |
| author_facet | Tuan, Tran |
| contents | <p>In this paper, we present a generalized, two-sided extension of Steffensen’s in<br>equality. By introducing a scaling parameter derived from the bounds of the weight<br>function, we establish rigorous upper and lower integral bounds for non-negative,<br>integrable functions that exhibit either monotonically decreasing or monotonically<br>increasing behavior. While the classical formulation strictly confines the weight<br>function to the interval [0,1], our approach generalizes this result by scaling the<br>bounded weight function, allowing g(x) ∈ [c,d] with c ≥ 0, and defining the scaled<br>parameter k = 1<br>d <br>b<br>ag(x)dx. This analytical tool serves as a foundational lemma for<br>advanced integral theories.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20328274 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | An Extension of Steffensen's Inequality Tuan, Tran Mathematical analysis Pure mathematics Applied mathematics Mathematics/history Mathematics/methods Mathematics/statistics & numerical data <p>In this paper, we present a generalized, two-sided extension of Steffensen’s in<br>equality. By introducing a scaling parameter derived from the bounds of the weight<br>function, we establish rigorous upper and lower integral bounds for non-negative,<br>integrable functions that exhibit either monotonically decreasing or monotonically<br>increasing behavior. While the classical formulation strictly confines the weight<br>function to the interval [0,1], our approach generalizes this result by scaling the<br>bounded weight function, allowing g(x) ∈ [c,d] with c ≥ 0, and defining the scaled<br>parameter k = 1<br>d <br>b<br>ag(x)dx. This analytical tool serves as a foundational lemma for<br>advanced integral theories.</p> |
| title | An Extension of Steffensen's Inequality |
| topic | Mathematical analysis Pure mathematics Applied mathematics Mathematics/history Mathematics/methods Mathematics/statistics & numerical data |
| url | https://doi.org/10.5281/zenodo.20328274 |