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New analogues of Hilbert integral inequality of three variables


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Authors

  • Nizar Kh. Al-Oushoush Department of Mathetics, Faculty of Science, Al-Balqa Applied University, P.O. Box 19117, Salt, Jordan

Keywords:

Hilbert’s integral inequality, Hölder inequality, Equivalent Forms. 2000 Mathematics Subject Classification: 26D15.

Abstract

In this paper, we apply Hölder inequality, use the special functions Gamma and Beta functions as tools, and use special substitutions to evaluate the integrals that appears in the main results to give a new form for Hilbert Integral Inequality for three variables. The reverse form and equivalent forms of the inequality in theorem 1 are also obtained. The constant we obtained is the best constant.

References

Nizar, Al-O. Kh., Azar, L. E., and Ahmad H. A. Bataineh, A Sharper Form of Half-Discrete Hilbert Inequality Related to Hardy Inequality, Filomat, 32 (19), (2018), 6733–6740.

Yang, B., The norm of operator and Hilbert-Type Inequalities, Scince press, Beijing, China, (2009).

Hardy, G. H., Littlewood, J. E., and Polya, G., “Inequalities”, Cambridge Univ. Press, London, (1952).

Azar, L. E., Tow new forms of Hilbert integral inequality, Math. Inequal. Appl. 17, (2014).

Krnić, M., A refined discrete Hilbert inequality via the Hermite-Hadamard inequality, Comput. Math. Appl. 63, (2012), 1587–1596.

Krnic, M., Mingzhe, G., Pecaric, J., and Xuemei, G., On the best constant in Hilbert’s inequality, Math. Inequal. Appl. 8 (2), 2005 317–329.

Krnić, M. J., Pecarić, Extension of Hilbert’s inequality, J. Math. Anal. Appl. 324, (2006), 150–160.

Krnić, M. J. Pecarić, General Hilbert’s and Hardy’s inequalities, Math. Inequal. Appl. 8, (2005), 29–52.

Batbold, T., and Azar, L. E., A new form of Hilbert Integral inequaltity, 12 (2), (2018), 379–390.

Al-Oushoush, N. K., New Discrete Form of Hilbert Inequality for Three Variables, Journal of Mathematical Analysis, 13 (3), (2022), 56–67.

Al-Oushoush, N. K., A New Version of Hilbert Integral Inequality of Three Variables with Hyperbolic Sine Function, Journal of Inequalities and Special Functions, 13 (4), 1–11.

Batbold, T., and Azar, L. E., Discrete analogues of Hilbert integral inequalities for three variables, Journal of Inequalities and Special function, 9, (2018), 66–76

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Published

2023-07-18

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How to Cite

Nizar Kh. Al-Oushoush. (2023). New analogues of Hilbert integral inequality of three variables. Results in Nonlinear Analysis, 6(2), 75–87. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/266

Issue

Vol. 6 No. 2 (2023): volume 6 issue 2

Section

Articles

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