A Novel Variant of Milne’s Rule Inequalities on Quantum Calculus for Convex Functions with Their Computational Analysis (Journal of Nonlinear Modeling and Analysis, 2025)
In this investigation, we introduce a novel approach for establishing Milne’s type inequalities in the context of quantum calculus for differentiable convex functions. First, we prove a quantum integral identity. Wederive numerous new Milne’s rule inequalities for quantum differentiable convex functions. These inequalities are relevant in open Newton-Cotes formulas,as they facilitate the determination of bounds for Milne’s rule applicable todifferentiable convex functions in both classical and $q$-calculus. In addition,we conduct a computational analysis of these inequalities for convex functionsand provide mathematical examples to demonstrate the validity of the newlyestablished results within the framework of $q$-calculus.