New sequence spaces derived by the composition of binomial and quadruple band matrices

This thesis study consists of four chapters. In the first chapter, frequently used sequence spaces are mentioned by giving definition of sequence space. In the first part of the first chapter, basic definitions and theorems used throughout the thesis are given. Also, the notions of matrix transformations, matrix classes and dual space are mentioned. In the second part of the first chapter, literature summary is given. In the first part of the second chapter, four new sequence spaces b_0^(r,s) (Q),b_c^(r,s) (Q),b_∞^(r,s) (Q) and b_p^(r,s) (Q) derived by the composition of binomial and quadruple band matrices are constructed. These sequence spaces are linear isomorphic to classical sequence spaces and some inclusion relations are mentioned. In the second part of the second chapter, the Schauder bases of the new constructed sequence spaces are mentioned and their α-, β- and γ- duals are determined. In the third part of the second chapter, some matrix classes of those spaces are characterized. In the third chapter, the obtained results are given briefly. In the fourth chapter, some suggestions are given for further studies.