Simpson’s and Newton’s Type Inequalities for (α,m)-Convex Functions via Quantum Calculus

In this paper, we give the generalized version of the quantum Simpson’s and quantum Newton’s formula type inequalities via quantum differentiable $\left(\alpha ,m\right)$-convex functions. The main advantage of these new inequalities is that they can be converted into quantum Simpson and quantum Newton for convex functions, Simpson’s type inequalities $\left(\alpha ,m\right)$-convex function, and Simpson’s type inequalities without proving each separately. These inequalities can be helpful in finding the error bounds of Simpson’s and Newton’s formulas in numerical integration. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.