Some New Paranormed Sequence Spaces and α- Core
Abstract
In this study, we define new paranormed sequence spaces by combining a double sequential band matrix and a diagonal matrix. Furthermore, we compute the α-,β- and γ- 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),(q) and ∞(q). Finally, α-core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.
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