Abdulcabbar SONMEZ

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

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 ??, where 1 ≤ ? < ∞. Moreover, we obtainsome inclusion relations and Schauder basis of the space $b_p^{r,s}$(D). We also pinpoint ?-, ?- and?-duals of the space $b_p^{r,s}$(D)). Finally, we classify some matrix classes related to the space$b_p^{r,s}$(D).

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