On the Spaces of Nörlund Almost Null and Nörlund Almost Convergent Sequences

Abstract

In this article, the sequence spaces f_{0}(N^{t}) and f(N^{t}) are introduced as the domain of Nörlund mean in the spaces  f_0 and f of almost null and almost convergent sequences which are isomorphic to the spaces f_0 and f, respectively, and some inclusion relations are given. Additionally, alpha, beta and gamma duals of the sequence spaces f_{0}(N^{t}) and f(N^{t}) are determined. Finally, the classes (\lambda(N^{t}):\mu) and (\mu:\lambda(N^{t})) of matrix transformations are characterized for given sequence spaces  \lambda and \mu together with two Steinhaus type results.