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

New inequalities similar to Hardy-Hilbert's inequality

Namita DAS
Sayfa
153–166
Yayın Tarihi
2010-02-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The integral analogues of the main results are also given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality.
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Temel Bulgular & Veri:As applications, some particular results and the equivalent form are derived.
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Sonuç & Katkı:The integral analogues of the main results are also given.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hardy-Hilbert's inequality · Hölder's inequality · b-function.

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.

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.

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Bu Makaleye Atıf Yap

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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Kaynakça (8)

  1. Hardy G.H., Littlewood J.E. and Polya G., Inequalities, Cambridge University Press, Cambrige, 1952.
  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]