On Some New Paranormed Sequence Spaces

Abstract The sequence spaces c0 , c and `∞ 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 c0(u, p), c(u, p) and `∞(u, p). Let μ denote any of the spaces c0, c and `∞. We prove that μ(u, p) is linearly paranorm isomorphic to μ(p) and determine the α−, β− and γ− duals of the μ(u, p). Furthermore, the basis of c0(u, p) and c(u, p) are constructed. Finally, we characterize the matrix transformations from the spaces c0(u, p), c(u, p) and `∞(u, p) to the spaces c0(q), c(q), `(q) and `∞(q).