Abstract
In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.
Highlights
Academic Editor: Nicusor MinculeteReceived: 7 September 2021Accepted: 26 September 2021Published: 3 October 2021Publisher’s Note: MDPI stays neutralThe Hermite–Hadamard (H-H) inequality, which was independently found by C.Hermite and J
Inspired by the ongoing studies, we give the generalizations of the results proved in [33,39,41,59] by proving H-H trapezoid and midpoint type inequalities for preinvex functions using the concepts of ( p, q)-difference operators and ( p, q)-integral
We proved H-H type inequalities for preinvex functions using the ( p, q)-calculus setup
Summary
The Hermite–Hadamard (H-H) inequality, which was independently found by C. The phrase q-calculus binds mathematics and physics together It is employed in subjects including combinatorics, number theory, basic hypergeometric functions, orthogonal polynomials, and others, as well as relativity theory, mechanics, and quantum theory [25,26]. The authors used the π1 D p,q difference operator and the ( p, q)π1 -integral to generalize the results of [39] and show H-H type inequalities and their left estimates [56]. Inspired by the ongoing studies, we give the generalizations of the results proved in [33,39,41,59] by proving H-H trapezoid and midpoint type inequalities for preinvex functions using the concepts of ( p, q)-difference operators and ( p, q)-integral.
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