Symmetric Quantum Inequalities on Finite Rectangular Plane - Saad Ihsan Butt; Muhammad Nasim Aftab; Youngsoo Seol (Mathematics, 2024)
Finding the range of coordinated convex functions is yet another application for the symmetric Hermite–Hadamard inequality. For any two-dimensional interval <semantics>[a0,<mspace width="0.166667em"></mspace>a1]×[c0,<mspace width="0.166667em"></mspace>c1]⊆ℜ2</semantics>, we introduce the notion of partial <semantics>qθ</semantics>-, <semantics>qϕ</semantics>-, and <semantics>qθqϕ</semantics>-symmetric derivatives and a <semantics>qθqϕ</semantics>-symmetric integral. Moreover, we will construct the <semantics>qθqϕ</semantics>-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.