Generalized Ostrowski-Gruss Like Inequality on Time Scales - Faraz Mehmood; Asif Khan; Muhammad Shaikh (Sahand Communications in Mathematical Analysis, 2023)
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-Grüss 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.