Strictly and uniformly monotone sequential Musielak-Orlicz spaces

Characterizations of various monotonicity properties (UM, LUM, STM) in the sequential Orlicz spaces $l_\phi h_\phi$, for the Luxemburg norm $\parallel\cdot\parallel_\phi$, are considered (cf. [23]). It follows that the strong monotonicity (STM) and the uniform monotonicity (UM) do not coincide in general for the counting measure case. Some applications to (dominated) best approximation are also given.