Some new sequence spaces which include the spaces lp and l infinity

In the present paper, we introduce the sequence space apr of non-absolute type and prove that the spaces apr and lp are linearly isomorphic for 0 < p < oo. We also show that apr which includes the space Lp, is a p-normed space and a BK space in the cases of 0 < p < 1 and 1 < p < oo, respectively. Furthermore, we give some inclusion relations and determine the alfa-, beta- and gamma-duals of the space Op and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space arp to some of the known sequence spaces and to some new sequence spaces.