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L-norms and M-norms on Banach lattices, unit-norms and base norms on ordered vector spaces are well known. In this paper m- and $m_{≤}$-norms are introduced on ordered normed spaces. They generalize the notions of the M-norm and the order-unit norm, possess also some interesting properties and can be characterized by means of the constants of reproducibility of cones. In particular, the dual norm...