Document Type : Research Paper


1 Dawood UniDepartment of Mathematics, Samarkand State University, University boulevard 15, Samarkand 140104, Uzbekistan and Department of Mathematics, Dawood University of Engineering.

2 Technology, New M. A. Jinnah Road, Karachi-74800, Pakistan.versity of Engineering and Technology.

3 Department of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan.

4 Nabi Bagh Z. M. Govt. Science College, Saddar, Karachi-75270, Pakistan.


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.


Main Subjects

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