Quantum inequalities of Hermite-Hadamard type for \(r\)-convex functions (Q2034956)

Summary: In this present study, we first establish Hermite-Hadamard type inequalities for \(r\)-convex functions via \(q^{\kappa_2}\)-definite integrals. Then, we prove some quantum inequalities of Hermite-Hadamard type for product of two \(r\)-convex functions. Finally, by using these established inequalities and the results given by \textit{K. Brahim} et al. [Matematiche 70, No. 2, 295--303 (2015; Zbl 1342.26047)], we prove several quantum Hermite-Hadamard type inequalities for coordinated \(r\)-convex functions and for the product of two coordinated \(r\)-convex functions.