Symmetric Quantum Inequalities on Finite Rectangular Plane

Abstract

Finding the range of coordinated convex functions is yet another application for the symmetric Hermite–Hadamard inequality. For any two-dimensional interval [a0,a1]×[c0,c1]⊆ℜ2, we introduce the notion of partial qθ-, qϕ-, and qθqϕ-symmetric derivatives and a qθqϕ-symmetric integral. Moreover, we will construct the qθqϕ-symmetric Hölder’s inequality, the symmetric quantum Hermite–Hadamard inequality for the function of two variables in a rectangular plane, and address some of its related applications.