On Some New Normed Narayana Sequence Spaces

Abstract

In this paper, we first establish the regular matrix $N$ using Narayana numbers. Then, we create new normed sequence spaces $Z(N)$ using the matrix $ N$ and demonstrate that these spaces are linearly isomorphic to $Z$ where $Z\in\{c_0, c, \ell_p, \ell_\infty\}$. Additionally, we provide inclusion relations for the spaces $c_0(N)$, $c(N)$, $\ell_p(N)$, and $\ell_\infty(N)$. Furthermore, we construct the Schauder bases of the $c_0(N)$, $c(N)$, and $\ell_p(N)$. Finally, we compute the $\alpha$-, $\beta$-, and $\gamma$-duals of these spaces and characterize the classes $(Z(N),X)$ for the certain choice of the sequence space $X$.