B(r, s, t, u) - dvostruko sumabilni prostori nizova i matrične transformacije
Author
Tuğ, Orhan A.Mentor
Rakočević, Vladmir R.Committee members
Milovanović, Gradimir V.Đorđević, Dragan S.
Malkowsky, Eberhard
Đolović, Ivana
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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 subclass...es 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.