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Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 2

New inequalities similar to Hardy-Hilbert's inequality

Namita DAS
Pages
153–166
Publication Date
2010-02-01
DOI
—
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AI Summary & Key Takeaways

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

The integral analogues of the main results are also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality.
📊
Key Findings & Data:As applications, some particular results and the equivalent form are derived.
💡
Conclusion & Impact:The integral analogues of the main results are also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hardy-Hilbert's inequality · Hölder's inequality · b-function.

Abstract

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

Özet

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

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Cite This Article

DAS, N. (2010). New inequalities similar to Hardy-Hilbert's inequality. Turkish Journal of Mathematics, Cilt: 34 - Sayı: 2, 153–166. https://ajindex.com/articles/723364

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References (8)

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  2. Krylov V. I., Approximation Calculation of Integrals, Macmillan, New York, 1962.
  3. Kuang J., Applied Inequalities, Shangdong Science and Technology Press, Jinan, 2004.
  4. Krnic M. and Pecaric J., Extension of Hilbert’s inequality, J. Math. Anal. Appl., 324,(2006), 150-160.
  5. Mitrinovic D.S., Analytic Inequalities, Springer-Verlag Berlin, New York, 1970.
  6. Mitrinovic D.S., Pecaric J.E. and Fink A.M., Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Boston, 1991.
  7. Pachpatte B.G., On some new inequalities similar to Hilbert’s inequality, J. Math. Anal. Appl., 226,(1998), 166 Pachpatte B.G., Inequalities similar to certain extensions of Hilbert’s inequality, J. Math. Anal. Appl., 243,(2000), 227. Wang Z. and Guo D., An Introduction to Special Functions, Science Press, Beijing, 1979.
  8. Yang B. and Rassias T. M., On the way of weight coefficient and research for the Hilbert-type inequalities, Math. Ineq. Appl., 6(4)(2003), 625-658. Namita DAS P.G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar, Orissa, 751004 INDIA e-mail: [email protected] Srinibas SAHOO Department of Mathematics, Banki College, Banki, Orissa, 754008 INDIA e-mail: [email protected]