Annals of Communications in Mathematics

AbstractIn this article, we establish several integral inequalities under new parametric primitive exponential-weighted integral inequality assumptions. The generality and versa- tility of these assumptions allow our results to extend and unify existing frameworks in the literature. In total, eight theorems are formulated. To ensure completeness and accessibil- ity, detailed proofs are given for all the theorems.

AbstractIn this article, we revisit a well-known result from the literature that can be considered a variant of the Hardy integral inequality. First, we present a counterexample to demonstrate the invalidity of the current formulation. We then revise the result by identifying and addressing a gap in the original proof. Finally, as an additional contribution, we derive a new integral inequality.

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.