On the Paranormed Nörlund Sequence Space of Nonabsolute Type - Medine Yeşilkayagil; Feyzi Başar (Abstract and Applied Analysis)
Maddox defined the space ℓ(p) of the sequences x=(xk) such that ∑k=0∞‍|xk|pk<∞, in Maddox, 1967. In the present paper, the Nörlund sequence space Nt(p) of nonabsolute type is introduced and proved that the spaces Nt(p) and ℓ(p) are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the space Nt(p) are computed and the basis of the space Nt(p) is constructed. The classes (Nt(p):μ) and (μ:Nt(p)) of infinite matrices are characterized. Finally, some geometric properties of the space Nt(p) are investigated.