Schur–Ostrowski type theorems revisited

In this paper we extend Schur–Ostrowski theorem on Schur-convex functions from majorized vectors to separable ones. For this, we introduce a generalized Schur–Ostrowskiʼs condition. We apply the obtained result for cone orderings and group-induced cone orderings. Finally, we give some interpretations for absolutely weak majorization and for group majorization on the space of complex matrices.