Applications to Korovkin approximation theory of some types of convergence

Keywords; Korovkin Approximation Theorem, statistical convergence, rate of convergence, Szasz operator. This study consists of five chapters. In the first chapter, a short summary of the Korovkin approximation theorem was given. In the second chapter, all the definitions and theorems which are needed and mentioned are mentioned in detail. In the third chapter, the application of the modified discrete operator, which was previously described, to the Korovkin approximation theorem using -statistical uniform convergence was investigated. In the fourth chapter, we applied the newly defined Fibancci Dunkl analogue of Szasz operators to the Korovkin approximation theorem. Korovkin approximation was studied in weighted spaces. Then, rate of convergence was examined with various methods. In the fifth chapter, the application of the Fibancci Dunkl analogue of Szasz operators to the Korovkin approximation theorem was investigated. Rate of convergence was evaluated with modulus of continuity and the Lipschitz requirement.