Matrix transformations of Norlund–Orlicz difference sequence spaces of nonabsolute type and their Toeplitz duals

Abstract

AbstractIn this paper, the Nörlund–Orlicz difference sequence space $\mathcal{N}^{t}(\mathcal{F},\Delta^{m}_{n},u,q)$Nt(F,Δnm,u,q) of nonabsolute type is introduced as a domain of Nörlund means which is isomorphic to the space $\ell(p)$ℓ(p) and the basis of the space is constructed. Additionally, the α−, β−, and γ-duals of the spaces are computed and their matrix transformations are given. Finally, the properties like rotundity, modularity of the newly formed spaces are established.