Abstract. In this paper, we establish some new nonlinear integral inequalities of Gronwall-Bellman type. These inequalities generalize some famous inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some nonlinear ordinary differential and integral equations. More accurately we extend certain results which have been proved in A. Abdeldaim and M. Yakout [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.

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In this paper, we prove some new weighted Ostrowski and Trapezoid type inequalities with powers on time scales. The results will be proved by employing the generalized version of Montgomery identity with weights on time scales designed and proved for this purpose. As special cases, we will derive some new weighted discrete inequalities of Ostrowski and Trapezoid types which to the best of the authors' knowledge are essentially new.