On separation by h-convex functions

In the present paper, we establish the necessary and sufficient conditions under which two functions can be separated by h-convex function, in the case, when the function h is multiplicative. This result is related to the theorem on separation by convex functions presented in Baron, K. Matkowski, J. Nikodem, K. [A sandwich with convexity, Math. Pannon. 5 (1994), 139 144].