Abstract
In this article, we construct new sequence spaces by combining the integrated and differentiated sequence spaces with the binomial matrix. We first construct the properties of these new sequence spaces and we examine some inclusion relations. Furthermore, we determine $\alpha-$, $\beta-$ and $\gamma-$ duals of the integrated and differentiated sequence spaces separately and provide proofs for some of them. Additionally, we characterize some matrix classes associated with these new sequence spaces, along with the obtained results. Finally, we investigate some geometric properties of new integrated sequence spaces.
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