On some new paranormed euler sequence spaces and Euler Core

In this paper, the sequence spaces e r0 (u, p) and e r c (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 e r0 (u, p) and e r c (u, p) are linearly isomorphic to spaces c 0(p) and c(p), respectively. Furthermore, the .-, .- and .-duals of the spaces e r0 (u, p) and e r c (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 (e r0 (u, p): µ) has been characterized, where µ is one of the sequence spaces . ., c and c 0 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.