We discuss $k$-rotundity, weakly $k$-rotundity, C-$k$-rotundity, weakly

C-$k$-rotundity, $k$-nearly uniform convexity, $k$-$\beta $ property, C-I

property, C-II property, C-III property and nearly uniform convexity both

pointwisely and globally in Orlicz function spaces equipped with Orlicz

norm.

Applications to continuity for metric projection at a given point are given

in Orlicz function spaces with Orlicz norm.