Positive linear operators and statistical A-summability

This master thesis consists of three chapters. The first chapter was devoted to the introduction. In the second section, respectively, positive linear operators, statistical convergence and - statistical convergence were introduced and some of the results known about these concepts were given. Furthermore, classic Korovkin type theorem and Korovkin type theorem for periodic functions was proven using statistical convergence and - statistical convergence. In the first section of the third chapter some concepts about statistical - summability which are stronger than - statistical summability were introduced. In the second and third section Korovkin type approximation theorem for positive linear operators was proven using statistical - summability and convergence rate was calculated with the help of modulus of continuity. In the fourth section Korovkin type approximation theorem for positive linear operators examined using statistical - summability on continuous - periodic functions space on and this theorem was shown to be stronger than classical Korovkin type approximation theorem in this space. Finally, convergence rate of periodic functions was calculated with the help of modulus of continuity.