SOME GENERALIZATIONS OF THE SEQUENCE SPACE αRP

Abstract – In the present paper, the sequence space a(u, p) of a non-absolute type is introduced and it is proved that the space a(u, p) is linearly isomorphic to the Maddox’s space ( ). p Besides this, the basis is constructed and the α-, βand γ-duals are computed for the space a(u, p). Furthermore, some matrix mappings from a(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 a(u, p).