Abstract
The aim of this paper is to establish some new ( p , q ) -calculus of Hermite–Hadamard inequalities for the double integral and refinements of the Hermite–Hadamard inequality for ( p , q ) -differentiable convex functions.
Highlights
Quantum calculus is the study of calculus without limits and is sometimes called q-calculus
The ( p, q)-derivative and ( p, q)-integral were defined and some basic properties are given. They obtained some new result for the ( p, q)-calculus of several important integral inequalities
The ( p, q)-calculus is being investigated extensively by many researchers, and a variety of new results can be found in the literature [13,14,15,16,17,18] and the references cited therein
Summary
Quantum calculus is the study of calculus without limits and is sometimes called q-calculus.In q-calculus, we obtain the original mathematical formulas when q tends to one. The subject of q-calculus has many applications in the field of mathematics and other areas such as number theory, special functions, combinatorics, basic hypergeometric functions, orthogonal polynomials, quantum theory, mechanics, and the theory of relativity and physics. The ( p, q)-derivative and ( p, q)-integral were defined and some basic properties are given. They obtained some new result for the ( p, q)-calculus of several important integral inequalities. The ( p, q)-calculus is being investigated extensively by many researchers, and a variety of new results can be found in the literature [13,14,15,16,17,18] and the references cited therein
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