A new paranormed series space and matrix transformations

Abstract

Recently, Hazar and Sarigol have defined and studied the series space |C₋₁|_{p} for 1≤p<∞ in [1]. The aim of this study is to introduce a new paranormed space |C₋₁|(p), where p=(p_{k}) is a bounded sequence of positive real numbers, which extends the results of Hazar and Sarigol in [1] to paranormed space. Besides this, we investigate topological properties and compute the α-,β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|C₋₁|(p),μ) and (μ,|C₋₁|(p)), where μ is any given sequence spaces