F-statistical convergence and korovkin type theorems

This thesis consists mainly of three chapters. The first chapter has been devoted to introduction. In the second chapter, first of all the concepts of density and statistical convergence have been introduced. Then the classical Korovkin type theorem and the statistical Korovkin type theorem have been given. The rate of statistical convergence has been introduced and the rate of the statistical Korovkin type theorem has been calculated with the help of this concept. Furthermore, the concept of Bögel continuity has been introduced and the space of Bögel continuous functions, which covers the space of continuous functions, has been introduced. Thus, Korovkin type theorems for Bögel continuous functions have been given. In the third part, the concept of f-statistical convergence, which is stronger than the usual convergence and is defined with the help of an unbounded modulus function, has been introduced. Using this concept, Korovkin-type theorems on the space of continuous functions for positive linear operators in one and two variables have been given. Moreover, a Korovkin-type theorem for Bögel continuous functions has been given with the help of f-statistical convergence. Moreover, examples have been given to show that the results obtained are stronger than the classical cases. Finally, the rate of f-statistical convergence has been defined and the rates of f-statistical convergence of the obtained Korovkin type theorems has been calculated