Fibonacci weighted difference sequence space

In this master's thesis, which consists of six chapters, İlkhan's article [1] was taken as a basis, and in the third, fourth, fifth and sixth chapters, article [1] is opened in detail and turned into a Turkish source. In the first chapter, general information about the studies on sequence spaces is given. Fibonacci numbers and some of their properties were briefly mentioned. In the continuation, a brief summary of the other chapters of the thesis is presented. In the second chapter, the basic definitions, propositions and theorems that will be used in the thesis are expressed. In the third chapter, by giving the Fibonacci difference matrix, a space called Fibonacci weighted difference sequence space ℓ_{p}(w,F) is defined with the help of the domain of this matrix and some properties of this space are examined. In the fourth chapter, for p=1, the semi norms of the defined matrix operators from ℓ₁(w) space, which is a special case of Weighted sequence space ℓ_{p}(w), to ℓ₁(w,F) space, which is a special case of Fibonacci weighted difference sequence space ℓ_{p}(w,F), are given and the semi norms of some special matrix operators are presented. In the fifth chapter, the semi norms of matrix operators defined for p from weighted sequence space ℓ_{p}(w) to Fibonacci weighted difference sequence space ℓ_{p}(w,F) are examined and semi norms of some special matrix operators are given. In the sixth chapter, the lower bound for T operator defined from ℓ_{p}(w) space to ℓ_{p}(w,F) space for p≥1 is obtained and the lower bound is calculated for the Hilbert matrix operator, which is a special matrix operator.