Some Notes on the New Sequence Space b_p^(r,s) (D)

In this paper, we describe the sequence space b_p^insert ignore into journalissuearticles values(r,s); insert ignore into journalissuearticles values(D); originated by the composition of the Binomial matrix and generalized second order difference insert ignore into journalissuearticles values(triple band); matrix and indicate that the space b_p^insert ignore into journalissuearticles values(r,s); insert ignore into journalissuearticles values(D); is linearly isomorphic to the space l_p, where 1≤p<∞. Moreover, we obtain some inclusion relations and Schauder basis of the space b_p^insert ignore into journalissuearticles values(r,s); insert ignore into journalissuearticles values(D);. We also pinpoint α-, β- and γ-duals of the space b_p^insert ignore into journalissuearticles values(r,s); insert ignore into journalissuearticles values(D);. Finally, we classify some matrix classes related to the space b_p^insert ignore into journalissuearticles values(r,s); insert ignore into journalissuearticles values(D);.