SOME GENERALIZATIONS OF THE SEQUENCE SPACE rp a

In the present paper, the sequence space ar(u, p) of a non-absolute type is introduced and it is proved that the space ar(u, p) is linearly isomorphic to the Maddox’s space ??(p).Besides this, the basis is constructed and the ?-, B- and ?-duals are computed for the space ar(u, p). Furthermore, some matrix mappings from ar(u, p) to some sequence spaces are characterized. The final section of the paper is devoted to some consequences related to the rotundity of the space ar(u, p).