  We generalize some results of Borwein, Burke, Lewis, and Wang to mappings
with values in metric (resp. ordered normed linear) spaces. We define two
classes of monotone mappings between an ordered linear space and a metric space
(resp. ordered linear space): $K$-monotone dominated and cone-to-cone monotone
mappings. First we show some relationships between these classes. Then, we
study continuity and differentiability (also in the metric and $w^*$ senses) of
mappings in these classes.
