A study of new quantum Montgomery identities and general Ostrowski like inequalities

Abstract

The main objective of this paper is to analyze the Montgomery identities and Ostrowski like inequalities, within the framework of quantum calculus. The study utilizes qϖ3 and qϖ4 differentiable functions to establish two new Montgomery identities, which are essential for the development of our main results which are new quantum estimates of general Ostrowski type inequality. The study involves numerous techniques, including q-identities, Hölder-like inequalities, and the Jensen-Mercer inequality for convex mappings, to derive the main outcomes of the paper. Additionally, the study presents special cases, numerical validation, and graphical illustrations to support the main results. © 2024 The Author(s)