On Weighted Montgomery Identity for k Points and Its Associates on Time Scales

Abstract

The purpose of this paper is to establish a weighted Montgomery identity for $k$ points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for $k$ points. For $k=\mathrm{2},$ we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.