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Dynamic Littlewood-type inequalities

Authors: Ravi Agarwal, Martin Bohner and Samir Saker
Journal: Proc. Amer. Math. Soc. 143 (2015), 667-677
MSC (2010): Primary 26D10, 26D15, 34A40, 34N05, 39A12, 39A13
Published electronically: October 3, 2014
MathSciNet review: 3283653
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Abstract: In this paper, we present some dynamic inequalities on time scales. As special cases, these results contain and improve some integral inequalities and some discrete inequalities formulated by Littlewood in connection with some work on the general theory of orthogonal series.

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  • [1] Ravi P. Agarwal, Donal O'Regan, Martin Bohner, and Samir H. Saker, Some dynamic Wirtinger-type inequalities and their applications, Pacific J. Math. 252 (2011), no. 1, 1-18. MR 2862138 (2012j:26015),
  • [2] Moulay Rchid Sidi Ammi and Delfim F. M. Torres, Hölder's and Hardy's two dimensional diamond-alpha inequalities on time scales, An. Univ. Craiova Ser. Mat. Inform. 37 (2010), no. 1, 1-11. MR 2609350 (2011i:26034)
  • [3] Matloob Anwar, Rabia Bibi, Martin Bohner, and Josip Pečarić, Integral inequalities on time scales via the theory of isotonic linear functionals, Abstr. Appl. Anal. 2011, Art. ID 483595, 16 pp.. MR 2819769 (2012f:26024),
  • [4] Grahame Bennett, An inequality suggested by Littlewood, Proc. Amer. Math. Soc. 100 (1987), no. 3, 474-476. MR 891148 (88g:26022),
  • [5] Martin Bohner and Billûr Kaymakçalan, Opial inequalities on time scales, Ann. Polon. Math. 77 (2001), no. 1, 11-20. MR 1867033 (2003e:26022),
  • [6] Martin Bohner and Allan Peterson, Dynamic equations on time scales, An introduction with applications, Birkhäuser Boston Inc., Boston, MA, 2001. MR 1843232 (2002c:34002)
  • [7] Martin Bohner and Allan Peterson (eds.), Advances in dynamic equations on time scales, Birkhäuser Boston, Inc., Boston, MA, 2003. MR 1962542 (2004d:34003)
  • [8] Peng Gao, On an inequality suggested by Littlewood, J. Inequal. Appl. 2011, 2011:5, 10 pp.. MR 2819744 (2012f:26030),
  • [9] Wei Ming Gong, On a problem of Littlewood, J. Yiyang Teachers College 14 (1997), no. 5, 15-16 (Chinese, with English and Chinese summaries). MR 1655812
  • [10] Stefan Hilger, Analysis on measure chains--a unified approach to continuous and discrete calculus, Results Math. 18 (1990), no. 1-2, 18-56. MR 1066641 (91m:26027),
  • [11] J. E. Littlewood, Some new inequalities and unsolved problems, Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 151-162. MR 0222231 (36 #5283)
  • [12] Umut Mutlu Ozkan and Hüseyin Yildirim, Hardy-Knopp-type inequalities on time scales, Dynam. Systems Appl. 17 (2008), no. 3-4, 477-486. MR 2569514 (2010i:26036)
  • [13] Samir H. Saker, Opial's type inequalities on time scales and some applications, Ann. Polon. Math. 104 (2012), no. 3, 243-260. MR 2914534,
  • [14] Samir H. Saker, Some Opial dynamic inequalities involving higher order derivatives on time scales, Discrete Dyn. Nat. Soc. (2012), Art. ID 157301, 22. MR 2984232
  • [15] Adnan Tuna and Servet Kutukcu, Some integral inequalities on time scales, Appl. Math. Mech. (English Ed.) 29 (2008), no. 1, 23-29. MR 2445568 (2009e:26047),

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Additional Information

Ravi Agarwal
Affiliation: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, Texas 78363

Martin Bohner
Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri 65409-0020

Samir Saker
Affiliation: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Keywords: Littlewood's inequality, time scales, dynamic inequality
Received by editor(s): April 28, 2013
Published electronically: October 3, 2014
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2014 American Mathematical Society

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