Table of Content
Primitives
Open AccessArticleTheoretical Results on New Hardy-hilbert-type Inequalities
Christophe Chesneau
Annals of Communications in Mathematics 2025,
8 (2),
253-274
DOI: https://doi.org/10.62072/acm.2025.080209
AbstractHardy-Hilbert-type integral inequalities lie at the heart of mathematical analysis. They have been the subject of much research. In this article, we make a contribution to the field by examining two new two-parameter modifications of the classical Hardy-Hilbert integral inequality. We derive the closed-form expression of the optimal constant for each modification. We also present supplementary results, including one-function and primitive variants. All proofs are provided in full, with each step justified, to ensure the article is self-contained.
Open AccessArticleExtending and unifying Hardy-Hilbert-type integral inequalities involving primitives
Christophe Chesneau
Annals of Communications in Mathematics 2026,
9(1),
12
DOI: https://doi.org/10.62072/acm.2026.09012
Abstract. In this article, we extend and unify the framework of a modified Hardy-Hilbert-type integral inequality established by W. T. Sulaiman in 2010. Our approach differs from previous works by incorporating the primitives of the main functions, considering four types of denominators for the kernel function, and introducing four adjustable parameters. The proofs are presented in full detail and can be reproduced with only a minimal level of prior knowledge.