Rotundity structure of local nature for generalized Orlicz-Lorentz function spaces

Criteria for extreme points and rotund points in generalized Orlicz-Lorentz function spaces, which were introduced in Foralewski (2011) [27] are given. Some examples show that in these spaces the notion of rotund point is essentially stronger than the notion of extreme point. Finally, the criteria obtained in this paper are interpreted in the case of classical Orlicz-Lorentz spaces. Results of this paper are related to the results from Carothers et al. (1992) [9], Kamińska (1990) [4], Foralewski et al. (2008) [26].