On some topological properties of generalized difference sequence spaces defined by modular sequence

In this study, we define some generalized difference sequence spaces by Modular sequence spaces and we examine some properties of these sequence spaces. We also give some inclusion relations between these spaces. In the first part of this thesis consisting of three chapters, some basic concepts related to the subject are given. In the second chapter, the basic concepts used throughout the thesis are given. Also, the concepts of difference sequence spaces, generalized difference sequences spaces, Orlicz function l_M (p) sequences space and Modular sequence space are defined and some theorems related to these and their topological properties are examined. In the third chapter, we define the new difference sequence spaces l_λ^M (∆^m,u,p) and l_N^λ (∆^m,u,p) where of Orlicz function M=(M_k ) and N=(N_k ) such that M_k and N_k be mutually complementary for each k. We also examine some topological properties of the sequence spaces and some inclusion relations between these spaces.