Property (k-β) of Musielak-Orlicz and Musielak-Orlicz-Cesaro spaces

In this paper, we investigate the geometric property (k-beta) for any fixed integer k1 of the space l phi((En)) generated by a Musielak-Orlicz function phi and a sequence (En) of finite dimensional spaces En, nN, equipped with both the Luxemburg and the Amemiya norms. As a consequence, we obtain the property (k-beta) of Musielak-Orlicz-Cesaro spaces ces phi using the approach recently considered by Saejung. Some applications to the Cesaro sequence spaces of order and Cesaro difference sequence spaces of order m are also noted.