Some new paranormed difference sequence spaces and weighted core

In this study, we define new paranormed sequence spaces by combining a generalized weighted mean and a difference operator. Furthermore, we compute the αα-,ββ- andγγ- duals and obtain bases for these sequence spaces. Besides this, we characterize the matrix transformations from the new paranormed sequence spaces to the spaces c0(q),c(q),ℓ(q)c0(q),c(q),ℓ(q) and ℓ∞(q)ℓ∞(q). Finally, weighted core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.