Orlicz spaces comprise an important class of Banach spaces that generalize Lebesgue spaces with a richer geometric structure. On the other hand, local uniform rotundity is one of the key concepts in the geometry of Banach spaces, playing an intermediary role between geometric properties. It reflects a refined rotundity and reveals the fine geometric structure of the space. In this study, we characterize the local uniform rotundity and some of its variations for Orlicz spaces equipped with the $s$-norms. These norms, introduced by M. Wis{\l}a, form a broad class that includes the classical Luxemburg and Orlicz norms. Thus, our results provides a comprehensive generalization to results obtained in the classical cases.

This talk is based on a joint work with Serap \"{O}ztop.

This study was funded by the Scientific and Technological Research Council of Turkey (TUBITAK), project number 123F368.