Let $(X,\Sigma,\mu)$ be a non-atomic, $\sigma$-finite, and complete measure space. Let $L^\Phi(X,\Sigma,\mu)$ be the Orlicz space generated by an Orlicz function.

In this talk, we examine $s$-norms, which are more general than the Orlicz, Luxemburg, and $p$-Amemiya norms. We also classify $s$-norms with respect to a constant. Then, based on this classification, we examine some properties of the $s$-norms.

This study is joint work with Serap Öztop, Esra Başar, Badik Hüseyin Uysal. This study was funded by the Scientific and Technological Research Council of Turkey (TUBITAK), project number 123F368.