We give a new Hermite–Hadamard inequality for a function which is semiconvex of rate on the coordinates. This generalizes some existing results on Hermite–Hadamard inequalities of S. S. Dragomir. In addition, we explain the Hermite–Hadamard inequality from the point of view of optimal mass transportation with cost function , where is semiconvex of rate on the coordinates and , .
"Hermite–Hadamard inequality for semiconvex functions of rate $(k_1,k_2)$ on the coordinates and optimal mass transportation." Rocky Mountain J. Math. 50 (6) 2011 - 2021, December 2020. https://doi.org/10.1216/rmj.2020.50.2011