Some Notes on the New Sequence Space $b_p^{r,s}$

Abstract

In this paper, we describe the sequence space $b_p^{r,s}$(D) originated by the composition of theBinomial matrix and generalized second order difference (triple band) matrix and indicate thatthe space $b_p^{r,s}$(D) is linearly isomorphic to the space 𝑙𝑝, where 1 ≤ 𝑝 < ∞. Moreover, we obtainsome inclusion relations and Schauder basis of the space $b_p^{r,s}$(D). We also pinpoint 𝛼-, 𝛽- and𝛾-duals of the space $b_p^{r,s}$(D)). Finally, we classify some matrix classes related to the space$b_p^{r,s}$(D).