Quantum calculus approaches to Ostrowski-type inequalities for strongly n-polynomial convex functions with applications in quantum physics

Abstract

This article aims to establish a new generalization of $q$-Ostrowski-type inequalities within the class of strongly $n$-polynomial convex functions by utilizing quantum calculus techniques, such as ${}_a{D}_q$- and ${}^b{D}_q$-derivatives, as well as $q_a$- and $q^b$-integrals. To improve the accuracy of these bounds, we utilize several mathematical quantum inequalities, including $q$-Hölder’s inequality and the $q$-power mean inequality. We derive some special cases from our main results and reproduce known results under specific conditions. The paper emphasizes the significance of these inequalities by presenting detailed examples and graphical representations. These examples demonstrate their practical applications and validate the theoretical findings. Moreover, these inequalities have significant applications in statistical physics, where they contribute to refining entropy inequalities and thermodynamic bounds.