On Some New Paranormed Sequence Spaces

The sequence spaces c^ λ 0 , c^λ and ℓ^ λ ∞ have been recently introduced and studied by Mursaleen and Noman [ On the spaces of λ− convergent and bounded sequences, Thai J. Math. 8(2)(2010),311-329]. The main purpose of the present paper is to extend the results of Mursaleen and Noman to the paranormed case and is to work the spaces c^λ 0 (u, p), c^λ (u, p) and ℓ^λ ∞(u, p). Let µ denote any of the spaces c0, c and ℓ∞. We prove that µ^λ (u, p) is linearly paranorm isomorphic to µ(p) and determine the α−, β− and γ− duals of the µ^λ (u, p). Furthermore, the basis of c^λ 0 (u, p) and c^λ (u, p) are constructed. Finally, we characterize the matrix transformations from the spaces c^λ 0 (u, p), c^λ (u, p) and ℓ^λ ∞(u, p) to the spaces c0(q), c(q), ℓ(q) and ℓ∞(q).