Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable ψ-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.

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

“…In [41], Kunt et al found some (q 1 , q 2 ) analogues of H-H-type inequalities and midpoints. Cortez et al obtained the integral identities via the φ preinvex function in [42]. Using new ideas [41,43], in recent years, numerous authors have provided other refinements and extensions of the inequalities [44][45][46] of the H-H and Ostrowski types [18,38,44,[47][48][49][50][51][52][53].…”

Some (p, q)-Integral Inequalities of Hermite–Hadamard Inequalities for (p, q)-Differentiable Convex Functions

“…Recently, the concept of the (p, q) b -integral and (p, q) bderivative over finite intervals was proposed by Vivas-Cortez et al [29] in 2021. In the past few years, the topic of (p, q)-calculus has become interesting in various integral inequalities for many researchers, and the results of (p, q)-calculus can be found in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], and the references cited therein.…”