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.
Highlights
Introduction and PreliminariesInequalities play a pivotal role in almost all branches of mathematics
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
We present some applications to a Axioms 2021, 10, 283 special means of positive real numbers and twice (p, q)-differentiable functions that are in absolute value bounded
Summary
Inequalities play a pivotal role in almost all branches of mathematics. For instance, the inequalities arising from the convexity property of related functions have numerous applications in the study of qualitative theory of differential equations and partial differential equations (see, for example, the papers of [1,2] for more details). Zhang et al [8] obtained a new generalized q-integral identity and obtained several new q-analogues of a first order q-differentiable convex function. Several new variants of classical integral inequalities have been obtained using the concepts of post-quantum calculus. Awan et al [11] obtained a generalized (p, q)-integral identity and obtained several new (p, q)-analogues of trapeziumlike inequalities. Yu et al [13] derived several new (p, q)-analogues of some classical integral inequalities and discussed applications as well. The main motivation of this article is to 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. We hope that the ideas and techniques of this paper will inspire interested readers working in this field
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