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Journals / Maltepe Journal of Mathematics / 2026 / Volume: 8 Issue: 1

Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions

Christophe Chesneau(Université de Caen-Normandie)0000-0002-1522-9292
Pages
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Publication Date
2026-04-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The article provides detailed proofs and discussions that extend the classical theory of Hilbert-type inequalities to richer analytical frameworks.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article presents two new Hilbert-type integral inequalities.
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Key Findings & Data:These inequalities feature innovative kernel functions that combine the arctangent, maximum operator and geometric mean, depending on an adjustable parameter.
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Conclusion & Impact:The article provides detailed proofs and discussions that extend the classical theory of Hilbert-type inequalities to richer analytical frameworks.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Integral inequalities · kernel functions · Holder integral inequality

Abstract

This article presents two new Hilbert-type integral inequalities. These inequalities feature innovative kernel functions that combine the arctangent, maximum operator and geometric mean, depending on an adjustable parameter. We derive sharp integral bounds associated with these kernel functions and prove the optimality of the corresponding constant factors under minimal assumptions. The article provides detailed proofs and discussions that extend the classical theory of Hilbert-type inequalities to richer analytical frameworks.

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Cite This Article

Chesneau, C. (2026). Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions. Maltepe Journal of Mathematics, Volume: 8 Issue: 1. https://doi.org/10.47087/mjm.1756359

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