Simpson- and Newton-Type Inequalities for Convex Functions via (p,q)-Calculus

Abstract

In this paper, we establish several new (p,q)-integral identities involving (p,q)-integrals by using the definition of a (p,q)-derivative. These results are then used to derive (p,q)-integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.

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

“…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]. Studies relative to convexity and preinvex functions have applications such as maximizing the likelihood from multiple linear regression involving a Gauss-Laplace distribution [54][55][56][57][58].…”

Post quantum Ostrowski-type inequalities for twice $(p,q)$-differentiable convex functions

“…Recently, the concept of the (𝑝, 𝑞) 𝑏 -derivative and (𝑝, 𝑞) 𝑏 -integral of a continuous function on a finite interval was presented by Vivas-Cortez et al 46 in 2021. Currently, the topic of (𝑝, 𝑞)-calculus is being investigated extensively by many scientists, and some new results can be found in 47,48,49,50,51,52,53,54,55 and the references cited therein.…”

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.…”