Local uniform rotundity and weak local uniform rotundity of Musielak–Orlicz sequence spaces endowed with the Orlicz norm

Criteria for local uniform rotundity and weak local uniform rotundity of Musielak–Orlicz sequence spaces equipped with the Orlicz norm are given. Criteria in order that the subspace of order continuous elements equipped with the norm induced from the whole space is locally (weakly) uniformly rotund are also presented.