o:1628 B(r, s, t, u) - dvostruko sumabilni prostori nizova i matrične transformacije B(r, s, t, u) - summable double sequence spaces and matrix transformations: doctoral dissertation : doctoral dissertation sr 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 1025838313 91552101 7303 91552100 1025838313 2020-02-26T15:08:55.053Z 45 no 46 mentor Orhan A., 1985-, 29299047 Tuğ 2019 63 mentor Vladmir R. Rakočević 2019 63 član komisije Gradimir V. Milovanović 2019 63 član komisije Dragan S. Đorđević 2019 63 član komisije Eberhard Malkowsky 2019 63 predsednik komisije Ivana Đolović 2019 81 list 2669297 http://phaidrabg.bg.ac.rs/o:1628 no yes 4 2020-02-26T15:08:55.320Z 70 Funkcionalna analiza, Sumabilnost, Matrični domeni,Prostori dvostrukih nizova Functional Analysis, Summability, Matrix Domain, Double SequenceSpaces 517.98(043.3) P 140 1738 18A07 18A0701 2019