On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus

Abstract

In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter m∈ 0,1. Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established equalities for right-quantum differentiable α,m-convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature.

Keywords

• Simpson’s inequalities
• Newton’s inequalities
• quantum calculus
• (<i>α</i>, <i>m</i>)-convex functions