On some new binomial double sequence spaces

This thesis consists of five main chapters. In the first chapter, summability and sequence spaces theories are briefly acquainted. In the second chapter, the literature is summarized and basic definitions, concepts and lemmas are given. The third chapter is devoted to material and method. The fourth section of the thesis is the original. In this part, firstly the 4-dimensional binomial matrix is defined and it is shown that this matrix is RH-regular for $r.s>0$. Then, some new binomial double sequence spaces are constructed as the domains of the newly defined matrix on the classical double sequence spaces, some algebraic and topological properties of these spaces are investigated. In addition, $\alpha$-, $\beta(\vartheta)$- and $\gamma$-duals of some of these spaces were determined and finally, some matrix transformations from newly defined spaces to classical sequence spaces and vice versa were characterized. In the fifth chapter, results of this thesis and some related open problems are stated for readers.