Tuğ, Orhan A., 1985-, 29299047 https://phaidrani.ni.ac.rs/o:1628 cobiss:1025838313 thesis:7303 In this dissertation, some new double sequence spaces derived as the domain of the four-dimensional generalized difference matrix are investigated. In the first chapter; literature review and some needed definitions and theorems are given for the following chapters. In the second chapter; we investigate the double sequence and series spaces with their basic properties which are used in the following chapters. In the third chapter we define the four-dimensional generalized difference matrix B(r; s; t; u) and new double sequence spaces are introduced as the domain of that matrix. In the fourth chapter; we study those new spaces and calculate their beta and gamma dual. In the fifth chapter; four-dimensional matrix transformations on the new spaces are studied in terms of four-dimensional dual summability methods for double sequences. Moreover, the characterization of some new four-dimensional matrix classes is also given. In the sixth chapter; as an application, the subclasses of compact operators on our new spaces were characterized by applying the Hausdorff measure of noncompactness of operators on B-summable double sequence spaces. In the seventh chapter; results of this thesis and some related open problems were stated. Biografija: list. [82];Bibliografija: listovi 77-81. Datum odbrane: 17.10.2019. Functional аnalysis info:eu-repo/semantics/bachelorThesis http://creativecommons.org/licenses/by-nc-nd/2.0/at/legalcode 2019 Rakočević, Vladmir R. Milovanović, Gradimir V. Đorđević, Dragan S. Malkowsky, Eberhard Đolović, Ivana B(r, s, t, u) - dvostruko sumabilni prostori nizova i matrične transformacije 81 list 2669297 bytes srp