Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable <i>ψ</i>-Preinvex Functions and Applications

Abstract

The main motivation of this article is derive a new post-quantum integral identity using twice (p, q)-differentiable functions. Using the identity as an auxiliary result, we will obtain some new variants of Hermite–Hadamard’s inequality essentially via the class of ψ-preinvex functions. To support our results, we offer some applications to a special means of positive real numbers and twice (p, q)-differentiable functions that are in absolute value bounded as well.

Keywords

• Hermite–Hadamard inequality
• Hölder’s inequality
• power mean inequality
• <i>ψ</i>-preinvex functions
• post-quantum calculus
• special means