On Some New Paranormed Lucas Sequence Spaces and Lucas Core

Abstract

The sequence spaces $c_{0}(\hat{L}), c(\hat{L}), \ell_{\infty}(\hat{L}) $ and $\ell_{p}(\hat{L})$ have been recently introduced and studied by Karakaç and Karabudak. The aim of this paper is to extend the results of Karakaç and Karabudak to the paranormed case and is to work the spaces $c_{0}(\hat{L},p), c(\hat{L},p), \ell_{\infty}(\hat{L},p) $ and $\ell(\hat{L},p)$. Furthermore, Lucas core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.