On the refinements of some important inequalities via $(p,q)$-calculus and their applications

Abstract

We establish some interesting refinements of the $(p,q)$ ( p , q ) -Hölder integral inequality and the $(p,q)$ ( p , q ) -power-mean integral inequality. As applications, we show that some existing $(p,q)$ ( p , q ) -integral inequalities can be improved by the results obtained in this paper.

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.…”

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

“…Kunt et al [12] obtained some (p, q)-analogues of Hermite-Hadamard and mid-point type inequalities. Yu et al [13] derived several new (p, q)-analogues of some classical integral inequalities and discussed applications as well. Definition 3.…”