Some new post‐quantum integral inequalities involving multi‐parameter and their applications

Abstract

In this paper, we establish a generic identity for (p, q)-differentiable functions involving multi-parameter. Using this identity as an auxiliary result, we derive some new post-quantum fundamental integral inequalities, including Simpson-type and Hermite-Hadamard-type pertaining n-polynomial convex functions. Also, by considering the boundedness and the Lipschitz condition of (p, q)-differentiable functions further results are given. Finally, in order to show the significance of our results, we present two illustrative examples and some applications to special means for different positive real numbers.

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.…”

Multivalent Functions and Differential Operator Extended by the Quantum Calculus

“…In addition, special functions (see [7,8]) have associated with this calculus, especially the queen of special functions: Mittag-Leffler function (see [9][10][11][12]). The quantum calculus (q-calculus) has tremendous applications in different fields, for example, integral inequalities [13], summability [14], approximation and polynomials [15], and sequence spaces [16].…”