Matrix Hermite–Hadamard type inequalities for bivariate convex functions

Considering convexity as well as matrix convexity for bivariate functions, we investigate the well-known Hermite–Hadamard inequality. In the case of separately convex bivariate functions, we present some majorization and norm inequalities. In the case of matrix convexity, a series of matrix inequalities are presented for bivariate matrix functions. Our results generalize some previous studies concerning Hermite–Hadamard inequality.