Convergent Sequences and Statistical Limit Points

In the present thesis, we prepare a summary of the existing theory of statistical, lacunary statistical, 𝜆���-statistical, 𝐴���-statistical limit points and some related topics for sequences of real numbers by using different research papers. In Chapter 1, you can find a summary of the existing theory of convergent sequences. The real number sequences and some of their important properties are all given in this chapter. In Chapter 2, we give the definitions and some important properties of statistical convergence, lacunary, 𝜆��� and 𝐴���-statistical convergence. In this chapter we also discuss implication and inclusion relations between these new type convergences. All implications and inclusions are illustrated by examples. Chapter 3, is devoted to the main work of this thesis. This chapter starts with the definitions of statistical limit point and statistical cluster point and continue with the discussion of similarities and differences between statistical and ordinary limit points of sequences of real numbers. Later the same study is repeated for lacunary statistical, 𝜆���-statistical and 𝐴���-statistical limit points for sequences of real numbers. Keywords: Statistical convergence, lacunary statistical convergence, 𝜆���-statistical convergence, 𝐴���-statistical convergence, statistical limit points, lacunary statistical limit points, 𝜆���-statistical limit points, 𝐴���-statistical limit points.