On Some Properties Paranormed Sequence Spaces Generated by Generalized Sequence Means and Core Theorems

Ali Karaisa, Ümit Karabıyık

Abstract

Recently, Mursaleen and Noman constructed newsequence spaces by using a matrix domain over a normed space. Theyalso studied some topological properties of these spaces.  In thiswork, we generalize the normed sequence space defined by Mursaleenand Noman to paranormed space. Furthermore, we introduce newsequence space over the paranormed space by using the expansionmethod. Then, we investigate some topological properties. Finally,generalized means core of a complex-valued sequence has beenintroduced and we prove some inclusion theorems related to this newtype of core.