Some new sequence spaces defined by the double band matrix

This study consists of five chapters. In Chapter 1, we give some fundamental definitions and theorems and give some information about Fibonacci numbers and present the works done on this subject. In Chapter 2, we define the ℓ_{p}(T) sequence space, where 1≤p≤∞ by using a new band matrix and we examine some topological properties of this space. Finally, we give some inclusion relations about this space. In Chapter 3, we investigate the α-, β- and γ- duals of the space ℓ_{p}(T). In Chapter 4, we analyze the matrix mappings from the space ℓ_{p}(T) to the spaces ℓ_{∞}, c, c₀ and ℓ₁. In the last chapter, we give some geometrical properties of the space ℓ_{p}(T).