Bounded and convergent sequence space derived from Fibonacci matrices and Nörlund

This thesis consists of five chapters. A new triangular matrix is obtained by multiplying the Nörlund matrix with the generalized Fibonacci bant matrix. The domain of this new triangular matrix on the sequence spaces which formed bounded and convergent series are obtained and defined as bsG and csG, respectively. At the same time, the properties of these spaces are examined. In the first part, the purpose and scope of the study are stated. In the second part, basic definitions and concepts related to the subject are given. In the third section, bsG and csG sequence spaces are defined. The spaces in which bsG and csG are isomorphic are determined. It is also shown that bsG and csG are linear space, normed space, Banach space. Inclusion relations between these spaces and other spaces are examined. In the fourth chapter, the ,  ve  duals of these two new spaces are constructed. It is given Schauder basis of csG. In the fifth section, the results characterizing the classes (bsG:), (csG:), (:bsG) and (:csG) are given such that  and  are two sequence spaces.