Some new sequence spaces derived by the domain of generalized difference matrix

Let denote any one of the classical spaces `1, c, c0 and `p of bounded, convergent, null and absolutely p-summable sequences, respectively, andb also be the domain of the generalized difference matrix B.r; s/ in the sequence space , where 1 p < 1. The present paper is devoted to studying on the sequence spaceb . Furthermore, the - and -duals of the spaceb are determined, and the Schauder bases for the spacesbc,bc0 and b` p are given, and some topological properties of the spacesbc0,b` 1 andb` p are examined. Finally, the classes .b 1 V 2/ and .b 1 V b 2/ of infinite matrices are characterized, where 1 2 f`1; c; c0; `p; `1g and 2 2 f`1; c; c0; `1g.