Symmetric Quantum Inequalities on Finite Rectangular Plane

Saad Ihsan Butt, Muhammad Nasim Aftab and Youngsoo Seol ()
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Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Muhammad Nasim Aftab: Department of Mathematics, Punjab Group of Colleges, Okara Campus, Okara 56101, Pakistan
Youngsoo Seol: Department of Mathematics, Dong-A University, Busan 49315, Republic of Korea

Mathematics, 2024, vol. 12, issue 10, 1-29

Abstract: Finding the range of coordinated convex functions is yet another application for the symmetric Hermite–Hadamard inequality. For any two-dimensional interval [ a 0 , a 1 ] × [ c 0 , c 1 ] ⊆ ℜ 2 , we introduce the notion of partial q θ -, q ϕ -, and q θ q ϕ -symmetric derivatives and a q θ q ϕ -symmetric integral. Moreover, we will construct the q θ q ϕ -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.

Keywords: coordinate convex functions; symmetric quantum calculus; symmetric quantum Hölder’s inequality; symmetric quantum Hermite–Hadamard inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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