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All Journal Hilbert Journal of Mathematical Analysis
Christophe Chesneau
University of Caen Normandie
Chemistry Control & Systems Engineering Engineering Mathematics Physics

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Contributions to three-dimensional Hardy-Hilbert-type integral inequalities Christophe Chesneau
Hilbert Journal of Mathematical Analysis Vol. 4 No. 1 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v4i1.50

Abstract

This article presents new extensions of the classical Hardy-Hilbert integral inequality involving primitive functions in three dimensions. Two complementary theorems are established, each providing a sharp upper bound for triple integrals associated with distinct kernel function structures. By introducing additional parameters, the proposed results offer greater flexibility and generality in the formulation and application of these inequalities.
A new integral inequality depending on the Lobachevskii function Christophe Chesneau
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.38

Abstract

This paper investigates a new logarithmic variant of the Hilbert integral inequality, beyond the standard homogeneous assumption. To this end, several theorems and propositions are proved, each of which gives new integral inequalities of independent interest. Remarkably, the Lobachevskii function appears quite naturally in some proofs, and forms an important part of the upper bound obtained. Several sharp examples are developed and discussed. A brief overview of the Lobachevskii function is given in the appendix.
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