Fibonacci almost convergence and core theorems

This work which focused on almost convergence and concept of core had four chapters. In addition, this study focused on the sequence spaces by Fibonacci Sequences.. In the first chapter, basic definitions and theorems were given and transformation sequence which was acquired by matrix was defined and characterization conditions of , and matrix classifications are given. Then, by the help of Banach limit, definitions of , space of all almost null sequences and , space of almost convergent sequences were given. The matrix classes of these spaces were also provided. In the second chapter, definitions of K-core and st-core and the coverage relations between these cores are given. In the third chapter, by defining Fibonacci sequence spaces, sequence space was created. Some inclusion relations of this space and matrix transformations related to sequence space were given. Furthermore, - core was defined and the location of this core was determined among the K- core, Banach- core and other cores . In the fourth chapter, sequence spaces , and created by the help of Fibonacci Null and Fionacci convergent sequences. The location of these spaces were determined among the other spaces. In addition, and duals and matrix transformations of these spaces were given. Key Words : Banach limits, almost convergence, statistical convergence, K-core, st-core.