Hermite-Hadamard's inequalities for multivariate g-convex functions

Refinements of generalized Hermite-Hadamard's inequalities for multivariate g -convex functions are given. Since special instances of the g -convex functions include the r -convex and the logarithmically convex functions, those inequalities also give refinements of the Hermite-Hadamard's ineqalities for these families of functions.