Locally uniform convexity in Musielak–Orlicz function spaces of Bochner type endowed with the Luxemburg norm

Criteria for locally uniform convexity of Musielak–Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. We also prove that, in Musielak–Orlicz function spaces generated by locally uniformly convex Banach space, locally uniform convexity and strict convexity are equivalent.