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

In this paper, we describe the sequence space b_p^(r,s) (D) originated by the composition of the Binomial matrix and generalized second order difference (triple band) matrix and indicate that the space b_p^(r,s) (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^(r,s) (D). We also pinpoint α-, β- and γ-duals of the space b_p^(r,s) (D). Finally, we classify some matrix classes related to the space b_p^(r,s) (D).

Keywords:

Matrix Transformation, Matrix Domain, Schauder Basis α- β- and γ-duals,

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