Improvement, generalizations and extensions of an integral inequality

Christophe Chesneau

Improvement, generalizations and extensions of an integral inequality

Abstract

This article is based on an integral inequality inspired by the work of S. Barza and E. C. Popa in 1998, which in turn draws on the work of G. H. Hardy. This inequality provides a sharp lower bound for the integral of the square of the derivative of a function, provided that a condition that relates the value of the function at zero to the integral of the function itself is satisfied. Our contributions present an improved version of this result as well as a parametric generalization and two extensions that overcome the initial restrictions. We also introduce two new inequalities involving an additional function. All proofs utilize fundamental integral techniques, making the work accessible and providing a potential foundation for further research.

Keywords

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Christophe Chesneau ^*
0000-0002-1522-9292
France

Publication Date

June 5, 2026

Submission Date

June 24, 2025

Acceptance Date

December 23, 2025

Published in Issue

Year 2026 Volume: 2 Number: 1

IZ

https://izlik.org/JA88LR26DB

Cite

RIS / Bibtex

APA

Chesneau, C. (2026). Improvement, generalizations and extensions of an integral inequality. Düzce Mathematical Research, 2(1), 58-66. https://izlik.org/JA88LR26DB

AMA

1.Chesneau C. Improvement, generalizations and extensions of an integral inequality. Düzce Mathematical Research. 2026;2(1):58-66. https://izlik.org/JA88LR26DB

Chicago

Chesneau, Christophe. 2026. “Improvement, Generalizations and Extensions of an Integral Inequality”. Düzce Mathematical Research 2 (1): 58-66. https://izlik.org/JA88LR26DB.

EndNote

Chesneau C (June 1, 2026) Improvement, generalizations and extensions of an integral inequality. Düzce Mathematical Research 2 1 58–66.

IEEE

[1]C. Chesneau, “Improvement, generalizations and extensions of an integral inequality”, Düzce Mathematical Research, vol. 2, no. 1, pp. 58–66, June 2026, [Online]. Available: https://izlik.org/JA88LR26DB

ISNAD

Chesneau, Christophe. “Improvement, Generalizations and Extensions of an Integral Inequality”. Düzce Mathematical Research 2/1 (June 1, 2026): 58-66. https://izlik.org/JA88LR26DB.

JAMA

1.Chesneau C. Improvement, generalizations and extensions of an integral inequality. Düzce Mathematical Research. 2026;2:58–66.

MLA

Chesneau, Christophe. “Improvement, Generalizations and Extensions of an Integral Inequality”. Düzce Mathematical Research, vol. 2, no. 1, June 2026, pp. 58-66, https://izlik.org/JA88LR26DB.

Vancouver

1.Christophe Chesneau. Improvement, generalizations and extensions of an integral inequality. Düzce Mathematical Research [Internet]. 2026 Jun. 1;2(1):58-66. Available from: https://izlik.org/JA88LR26DB