Generalized weighted Ostrowski and Ostrowski-Gr\"uss type inequalities on time scales via a parameter function

Abstract

We prove generalized weighted Ostrowski and Ostrowski--Gr\"uss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalities.