New Variants of Quantum Midpoint-Type Inequalities

Recently, there has been a strong push toward creating and expanding quadrature inequalities in quantum calculus. In order to investigate various avenues for quantum inquiry, a number of quantum extensions of midpoint estimations are studied. The goal of this research article is to discover novel quantum midpoint-type inequalities that are twice qξ2-differentiable for (α,m)-convex functions. Firstly, we obtain novel identity for qξ2-integral by employing quantum calculus tools. Then by using the auxiliary identity, we formulate new bounds by taking into account the known quantum Hölder and Power mean inequalities. An example is provided with a graphical representation to show the validity of obtaining results. The outcomes of this study clarify and expand earlier research on midpoint-type inequalities. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.