Mediterranean Journal of Mathematics

, Volume 13, Issue 2, pp 585–606 | Cite as

Weighted Hardy-Type Inequalities on Time Scales with Applications



In this paper, we will prove some new dynamic Hardy-type inequalities on time scales with two different weighted functions. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. The main results will be proved by employing Hölder’s inequality, Minkowski’s inequality and a chain rule on time scales. As special cases of our results, when the time scale is the real numbers, we will derive some well-known results due to Copson, Bliss, Flett and Bennett by a suitable choice of the weighted functions. We will apply the results to investigate the oscillation and nonoscillation of a half-linear second order dynamic equation on time scales.

Mathematics Subject Classification

26A15 26D10 26D15 39A13 34A40 34N05 


Hardy’s inequality Minkowski’s inequality time scales oscillation half-linear dynamic equations 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMansoura UniversityMansouraEgypt
  2. 2.Department of Mathematics, Faculty of ScienceFayoum UniversityFayoumEgypt
  3. 3.Department of MathematicsUniversity of Nebraska–LincolnLincolnUSA

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