Montgomery Identity and Ostrowski-Type Inequalities for Generalized Quantum Calculus through Convexity and Their Applications

Abstract

The celebrated Montgomery identity has been studied extensively since it was established. We found a novel version of the Montgomery identity when we were working inside the framework of p- and q-calculus. We acquire a Montgomery identity through a definite (p,q)-integral from these results. Consequently, we establish specific Ostrowski-type (p,q)-integral inequalities by using Montgomery identity. In addition to the well-known repercussions, this novel study provides an opportunity to set up new boundaries in the field of comparative literature. The research that is being proposed on the (p,q)-integral includes some fascinating results that demonstrate the superiority and applicability of the findings that have been achieved. This highly successful and valuable strategy is anticipated to create a new venue in the contemporary realm of special relativity and quantum theory. These mathematical inequalities and the approaches that are related to them have applications in the areas that deal with symmetry. Additionally, an application to special means is provided in the conclusion.

New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities

“…This theory knows a rapid development over the past few decades and have numerous applications in many areas of science such as quantum mechanics, approximation theory, statistics, and also in information theory, optimization, geometry function theory(GTF), as well as in cosmology and particle physics [34,35]. Quantum calculus was extended to (p, q)-calculus and recently to generalized quantum calculus [36].…”