Generalized statistical convergence and statistical limit points

Generalized Statistical Convergence and Statistical Limit PointsThis thesis consists of six chapters. The first chapter is devoted the introduction part.In chapter two, we give the concepts of natural density, statistical convergence, statistical boundedness, statistical Cauchy sequence, strong p-Cesàro summability and their basic properties and the relationships between them. Furthermore a theorem of multiplication of statistical convergent sequences and some results of this theorem are added.In chapter three, the concepts of ?-statistical convergence, strong (V,?)-summability are given; the relations between the set of ?-statistical convergent sequences S_{?} and the set of statistical convergent sequences S, and the set of strongly (V,?)-summable sequences [V,?] are examined. Also, the relations between the sets S_{?} and S_{?}, [V,?] and [V,?], S_{?} and [V,?] for various sequences ?,? in the class ? are examined. Furthermore some theorems and results of multiplication of ?-statistical convergent sequences are introduced.In chapter four, the concepts of statistical convergence of order ?, strongly p-Cesàro summability of order ? and the relations between them are given.In chapter five, the concepts statistical limit and statistical cluster points of a real number sequence and the relation between them are given.In the last chapter, the concepts statistical limit superior and limit inferior and the relation between them are given. Also, the relations between statistical limit superior (limit inferior) and ?_{x} the set of statistical cluster points are given.Key Words: Natural density, statistical convergence, statistical boundedness, strong p-Cesàro summability, ?-statistical convergence, statistical convergence of order ?, statistical limit and statistical cluster points, statistical limit superior and limit inferior.