On Some New Normed Narayana Sequence Spaces

Authors : Hacer Bilgin Ellidokuzoğlu

Pages : 40-50

Doi:10.53570/jnt.1407690

View : 66 | Download : 73

Publication Date : 2024-03-29

Article Type : Research Paper

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 $X$.
Keywords : Narayana numbers, Narayana matrices, sequence spaces, matrix transformations