Generalized Ostrowski-Gruss Like Inequality on Time Scales

In this paper, we present a generalization of the Montgomery Identity to various time scale versions, including the discrete case, continuous case, and the case of quantum calculus. By obtaining this generalization of Montgomery Identity  we establish results about the generalization of Ostrowski-Gr\"{u}ss like inequality to the several time scales, namely discrete case, continuous case and the case of quantum calculus. Additionally, we recapture several published results from different authors in various papers, thus unifying the corresponding discrete and continuous versions. Furthermore, we demonstrate the applicability of our derived consequence to the case of quantum calculus.

Keywords:

Ostrowski inequality , Gruss inequality , Ostrowski-Gruss inequality , Time scales , Quantum calculus