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

Abstract

This study aims to derive new Milne’s rule type inequalities for quantum differentiable (α, m)-convex
functions within the quantum calculus framework. It broadens the scope of integral inequalities, by
introducing quantum calculus version of H¨older 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 (α, m)-convex
functions.