On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus

Abstract

In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p,q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.

Special Issue Editorial “Symmetry in the Mathematical Inequalities”

“…Finally, explored certain convex or concave functions are explored, which are symmetric functions on the axis t = 1/2. M. J. Vivas-Cortez et al, in the paper "On Some New Simpson's Formula Type Inequalities for Convex Functions in Post-Quantum Calculus" [16], proved a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new Simpson's formula type inequalities for (p, q)-differentiable convex functions.…”