Abstract. In this paper, we prove some new dynamic inequalities from which some known dynamic inequalities on time scales, some integral and discrete inequalities due to Hardy, Copson, Chow, Levinson, Pachpatte Yang and Hwang will be deduced as special cases. Also, some new corresponding integral and discrete inequalities will be formulated. The results will be proved by employing the chain rule, integration by parts formula, Hölder's inequality and Jensen's inequality on time scales.Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40, 34N05.

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Abstract. In this paper, we will prove some new dynamic inequalities with two different weighted functions on a time scale. As special cases, the inequalities contain some dynamic inequalities on time scales and also involve some discrete inequalities formulated by Copson, Leindler, Bennett, Chen and Yang. The results will be proved by using Hölder's inequality and Minkowski's inequality on time scales.Mathematics subject classification (2010): 26D15, 34A40, 34N05, 39A12.

Abstract. In this paper, we prove some new diamond-alpha dynamic inequalities of Opial type with one and with two weight functions on time scales. These results contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case.Mathematics subject classification (2010): 39A10, 39A12, 26D15.