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The absolute Nörlund spaces Nu p k; ≥ 1; have more recently been introduced and studied by Hazar and Sargöl [On absolute Nörlund spaces and matrix operators, Acta Math. Sin. (Engl. Ser.), 34 (5) (2018), 812-826]: In the present paper, we characterize the classes of infinite matrix and compact operators transforming from Nu p k into X and obtain some identities or estimates for the Hausdorff measures of noncompactness, where X is one of the spaces '1, c and c0:. [ABSTRACT FROM AUTHOR]

In a way different from traditional methods, recently, new series spaces have been established by using absolute summability methods. Among these absolute summability methods, the absolute generalized Nörlund summability method |N, pn, qn, θn|k is extremely important as it includes several summability methods such as absolute Nörlund, weighted, Cesàro and Euler summability methods. Now, it is natural to ask behavior of the space derived by the absolute summability of generalized Nörlund means. The purpose of this study is to derive a more general series space including some well known spaces such as the spaces | N ˜ q θ | k , |Cα|k, |Cα, β|k, | N p θ | k and | E r θ | k , and to investigate its topological structure, α-, β- and γ-duals. Beside this, some matrix transformations related to these spaces have been characterized. [ABSTRACT FROM AUTHOR]