2-On statistical convergence of subsequences of statistically convergent sequences in metric spaces

In this thesis, using natural density in 2-metric spaces, the conditions under which subsequences of statistically convergent sequences converge and are statistically convergent are examined. Additionally, in 2-metric spaces, an inner product is defined on the equivalence classes with the help of an equivalence relation on the real-valued statistically convergent sequence space, C_st^2. C_st^2 metric space structure was achieved with a metric created with the help of this inner product. Additionally, with this metric, it has been shown that C_st^2 is a complete space and is a dense subspace of the set of convergent sequences (C_st^2,d_j). In this thesis; The concepts of symmetric continuous function, weak continuous function and weakly symmetric continuous function are reconsidered using the concept of natural density defined on subsets of natural numbers. The relationship between these new types of continuity concepts was examined and their properties were investigated.