New Riemann-Liouville generalizations for some inequalities of Hardy type
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DOI:
https://doi.org/10.26637/mjm402/012Abstract
In this paper, we present new generalizations for some integral results related to Hardy inequalities. For our results, some recent results of Hardy type and other interesting inequalities of integer order of integration can be deduced as some special cases.
Keywords:
Integral inequalities, Riemann-Liouville integral, Hardy ineqalityMathematics Subject Classification:
26D15, 26D10- Pages: 277-283
- Date Published: 01-04-2016
- Vol. 4 No. 02 (2016): Malaya Journal of Matematik (MJM)
S. Abramovich, K. Knlic, J. Pecacard, E. Presson: Some new refined Hardy type inequalities with general Kernels and measures, Aequat. Math., 79 (2010), 157-172. DOI: https://doi.org/10.1007/s00010-010-0011-8
Y. Bicheng, Z. Zhuohuaz, L. Debnath: On new generalizations of Hardy's integral inequality, J. Math. Anal. Appl., 217 (1998), 321-327. DOI: https://doi.org/10.1006/jmaa.1998.5758
W.S. Cheung, Z. Hanjs, J. Pecaric: Some Hardy-type inequalities, J. Math. Anal. Appl., 250 (2000), 621-634. DOI: https://doi.org/10.1006/jmaa.2000.7006
Z. Dahmani: About some integral inequalities using Riemann-Liouville integrals, General Mathematics, 20(4) (2012), 63-69.
R. Gorenflo, F. Mainardi: Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien, (1997), 223-276. DOI: https://doi.org/10.1007/978-3-7091-2664-6_5
Z. Hanjs, C.E.M. Pearce, J. Pecaric: Multivariate Hardy-type inequalities. Tamkang J. Math., 31 (2000), $149-158$. DOI: https://doi.org/10.5556/j.tkjm.31.2000.407
G.H. Hardy: Note on a theorem of Hilbert, Math. Z., 6 (1920), 314-317. DOI: https://doi.org/10.1007/BF01199965
G. H. Hardy: Notes on some points in the integral calculus, Messenger Math., 57 (1928), 12-16.
G.H. Hardy, J.E. Littlewood, G. Polya: Inequalities. Cambridge University Press, Cambridge, 1959.
A. Kufner, L. Maligranda, L.E. Persson: The Hardy inequality, about its history and some related results, Vydareatesky Sevis Publising House, Pilsen, 2007.
A. Kufner, L. Maligranda, L.E. Persson: The prehistory of the Hardy inequality, Amer. Math. Monthly, 113 (8) (2006), 715-762. DOI: https://doi.org/10.2307/27642033
N. Levinson: Generalizations of an inequality of Hardy, Duke Math. J., 31 (1964), 389-394. DOI: https://doi.org/10.1215/S0012-7094-64-03137-0
B.G. Pachpatte: On some generalizations of Hardy's integral inequality, J. Math. Anal. Appl., 234(1) (1999), 15-30. DOI: https://doi.org/10.1006/jmaa.1999.6294
S. Wu, B. Sroysang and S. Li: A further generalization of certain integral inequalities similar to Hardy's inequality. J. Nonlinear Sci. Appl., 9 (2016), 1093-1102. DOI: https://doi.org/10.22436/jnsa.009.03.37
M.Z. Sarikaya, H. Yildirim: Some Hardy type integral inequalities. JIPAM Journal, 7(5), Art. 178, (2006), 1-5.
B. Sroysang: A generalization of some integral inequalities similar to Hardy's inequality, Math. Aeterna, 3 (2013), 593-593. DOI: https://doi.org/10.1155/2013/925464
W.T. Sulaiman: Reverses of Minkowski's, Hölder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci., 1(1), (2012), 14-24.
W.T. Sulaiman: Some Hardy type integral inequalities. Appl. Math. Letters, 25(2012), 520-525. DOI: https://doi.org/10.1016/j.aml.2011.09.050
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