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Dergiler / Constructive Mathematical Analysis / 2026 / Volume: 8 Issue: 2

Study of some new one-parameter modifications of the Hardy-Hilbert integral inequality

Christophe Chesneau(Université de Caen-Normandie)0000-0002-1522-9292
Sayfa
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Yayın Tarihi
2025-06-15
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Thus, this work contributes to the ongoing development of Hardy-Hilbert-type inequalities by presenting new generalizations and providing rigorous mathematical justification for each result.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:One of the pillars of mathematical analysis is the Hardy-Hilbert integral inequality.
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Temel Bulgular & Veri:In this article, we advance the theory by introducing several new modifications of this inequality.
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Sonuç & Katkı:Thus, this work contributes to the ongoing development of Hardy-Hilbert-type inequalities by presenting new generalizations and providing rigorous mathematical justification for each result.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hardy-Hilbert integral inequality · power function · beta function

Abstract

One of the pillars of mathematical analysis is the Hardy-Hilbert integral inequality. In this article, we advance the theory by introducing several new modifications of this inequality. They have the property of incorporating an adjustable parameter and different power functions, allowing for greater flexibility and broader applicability. Notably, one modification has a logarithmic structure, offering a distinctive extension to the classical framework. For the main results, the optimality of the corresponding constant factors is shown. Additional integral inequalities of various forms and scopes are also established. Thus, this work contributes to the ongoing development of Hardy-Hilbert-type inequalities by presenting new generalizations and providing rigorous mathematical justification for each result.

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Bu Makaleye Atıf Yap

Chesneau, C. (2025). Study of some new one-parameter modifications of the Hardy-Hilbert integral inequality. Constructive Mathematical Analysis, Volume: 8 Issue: 2. https://doi.org/10.33205/cma.1698981

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