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.