Some Milne’s rule type inequalities for convex functions with their computational analysis on quantum calculus

Abstract

In this paper, we establish some new Milne?s type inequalities for the differentiable convex functions in quantum calculus (q-calculus). We prove q-integral identity first and then we prove some new Milne?s type inequalities for q-differentiable convex functions. These inequalities play an important role in Open-Newton?s Cotes formulas. Furthermore, we give the computational analysis of these inequalities for convex functions and prove that the bounds of this paper are better than the existing ones. Ultimately, we provide some mathematical examples to show the validity of newly establish inequalities in q-calculus.

Topics & Concepts