Quantum Milne type inequalities for (α,m)-convex function with their computational analysis

This study aims to derive new Milne?s rule type inequalities for quantum differentiable (?, m)-convex functions within the quantum calculus framework. It broadens the scope of integral inequalities, by introducing quantum calculus version of H?lder inequality and power mean inequality. Furthermore the study introduces a more direct and less restrictive proof strategy for establishing these inequalities. We established quantum inequalities and validate their correctness through numerical examples. Our finding enhance the understanding of quantum inequalities and their comparative analysis for (?, m)-convex functions.