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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.

New existence results (for positive solutions) for continuous and discrete boundary value problems to the one-dimension p -Laplacian are presented in this paper. Here we use a well-known fixed point theorem in cones. Our results improve several recent results established in the literature. (2000): 34B15, 39A10. Key words and phrases: positive solutions, continuous and discrete boundary value problem, p -Laplacian, fixed point theorem in cones. c Ð , Zagreb Paper MIA-07-53 Mathematics subject classification

Abstract. In this paper, we prove some new dynamic inequalities of Hilbert type on time scales. From these inequalities, as special cases, we will formulate some special integral and discrete inequalities. The main results are proved using some algebraic inequalities, Hölder's inequality, Jensen's inequality and a chain rule on time scales.Mathematics subject classification (2010): 26D15, 34A40, 39A12, 34N05.

Abstract. In this paper we prove some new dynamic inequalities with two weight functions and some new dynamic inequalities with two unknown functions of Opial type on time scales. The main results will be proved by employing Hölder's inequality, the chain rule and some basic algebraic inequalities.Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40.