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In this paper, we introduce a new series space |N pθ |(μ) as the set of all series summable by the absolute Nörlund summability method, which includes the spaces l(μ),|Cλ|k and |Npθ| k of Maddox [Spaces of strongly summable sequences, Quart. J. Math. 18(1) (1967) 345-355], Sarlgöl [Spaces of series summable by absolute Cesàro and matrix operators, Comm. Math Appl. 7(1) (2016) 11-22], Hazar and Sarlgöl [On absolute Nörlund spaces and matrix operators, Acta Math. Sinica, (English Ser.) 34(5) (2018) 812-826], respectively. Also, we study its some algebraic and topological structures such as isomorphism, the α, β, γ duals, Schauder basis, and characterize certain matrix transformations on that space. © 2019 World Scientific Publishing Company. |
