On some new paranormed euler sequence spaces and Euler Core

In this paper, the sequence spaces e0r(u, p) and ecr (u, p) of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e0r(u, p) and ecr(u, p) are linearly isomorphic to spaces c0(p) and c(p), respectively. Furthermore, the α-, β- and γ-duals of the spaces e0r(u, p) and ecr (u, p) have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices (e0r(u, p): µ) has been characterized, where µ is one of the sequence spaces ℓ∞, c and c0 and derives the other characterizations for the special cases of µ. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.