On banach cores and statistical convergence

This thesis which is related to Banach cores and statistical convergence, has three chapters. In the first chapter, some preliminary definitions, concepts, and theorems which will also be needed in other chapters, are given. After then, defining matrix transformations by using infinite matrices; definitions of regularity, conservative, almost convergence, and Banach limits are mentioned. In addition some theorems and results about Banach limits are given.In the second chapter, the concept of core is briefly explained. Definitions of K-core, B-core and theorems which are derived from these mentioned cores are given. Moreover, the coverage relations between these two cores are examined.In the third chapter, the concept of statistical convergence, theorems which are related to this convergence and matrix classifications are given. Also, by explaining the concept of statistical core the coverage relations with other cores are examined.Key Words :Banach limits, almost convergence, statistical convergence, K-core ,B-core ,st-core .