2015
DOI: 10.7153/mia-18-18
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Converses of Copson's inequalities on time scales

Abstract: Abstract. In this paper, we will prove some new dynamic inequalities on a time scale T . These inequalities when T = N contain the discrete inequalities due to Bennett and Leindler which are converses of Copson's inequalities. The main results will be proved using the Hölder inequality and Keller's chain rule on time scales.Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40. 34N05.

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Cited by 10 publications
(18 citation statements)
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“…By the following theorem, the reverse of the Bennett's (or Leindler's) inequality ( 7) is unified in Saker et al 34 for the delta time scale calculus.…”
Section: Introductionmentioning
confidence: 98%
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“…By the following theorem, the reverse of the Bennett's (or Leindler's) inequality ( 7) is unified in Saker et al 34 for the delta time scale calculus.…”
Section: Introductionmentioning
confidence: 98%
“…Then the aforementioned Hardy-Copson inequalities have been unified to an arbitrary time scale in the book 23 and in the papers [24][25][26][27][28][29][30][31] for the delta time scale calculus. In the delta time scale calculus, the reverse Hardy-Copson type inequalities, which are called delta Bennett-Leindler inequalities, can be found in previous works 28,[32][33][34] for 0 < q < 1. These results are unifications of discrete and continuous Bennett-Leindler inequalities mentioned above except the ones in Renaud.…”
Section: Introductionmentioning
confidence: 99%
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“…We can refer to the surveys [1,33] and the monograph [2] for exhibition of these results. The aforementioned Hardy-Copson inequalities have been unified to an arbitrary time scale in the book in [3] and in the articles in [4,[34][35][36][37][38][39][40] by using delta time scale calculus.…”
Section: Introductionmentioning
confidence: 99%