Two-Sided Ostrowski-Type Inequalities on Time Scales Under Integrable Derivative Bounds

In this paper, we introduce new two-sided Ostrowski-type inequalities on arbitrary time scales. Using the delta derivative and delta integral operators, we obtain explicit bounds for the deviation of a function value from the mean delta integral, under the assumption that the delta derivative is bounded between two integrable functions. With additional monotonicity conditions on the bound functions, further refinement of the obtained estimates is possible. The results recover the classical continuous Ostrowski inequality, as well as its discrete and quantum counterparts on Z and qZ, as special cases.