B(r, s, t, u) - dvostruko sumabilni prostori nizova i matrične transformacije
Tuğ, Orhan A.
Faculty:University of Niš, Faculty of Science and Mathematics
Rakočević, Vladmir R.
Milovanović, Gradimir V.
Đorđević, Dragan S.
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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.View More
Keywords:Funkcionalna analiza, Sumabilnost, Matrični domeni, Prostori dvostrukih nizova; Functional Analysis, Summability, Matrix Domain, Double Sequence Spaces