Table of Content
Integral inequalities
Open AccessArticleIntegral Inequalities Under Diverse Parametric Primitive Exponential-weighted Integral Inequality Assumptions
Christophe Chesneau
Annals of Communications in Mathematics 2025,
8 (1),
43-56
DOI: https://doi.org/10.62072/acm.2025.080104
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.
Open AccessArticleOn Some Connections Between Hilbert and Hardy Type Integral Inequalities
Christophe Chesneau
Annals of Communications in Mathematics 2025,
8 (3),
363-378
DOI: https://doi.org/10.62072/acm.2025.080303
ABSTRACT. This article investigates some new connections between the Hilbert and Hardy integral inequalities. In particular, two general theorems are established, both based on integral terms derived from those used in these two famous inequalities. They have the property of depending on two functions and one modulable parameter. Applications and examples are given to specific cases combining Hilbert and Hardy type integral inequalities. Emphasis is placed on a particular weighted integral term, showing how our results can be used to improve what can be obtained with some classical integral inequalities in the literature.