Korovkin type approximation theorems via power series method

This thesis consists of four chapters. First, some basic definitions that will be used throughout this thesis are given. Also, with the help of classical convergence, Korovkin theorems are stated for positive linear operators defined on the space of continuous functions defined on a compact set of real numbers, the space of continuous and 2π-periodic functions and the space H_w, respectively. An example is given which satisfies the theorems we have stated in the given spaces. Then, with the help of the power series method, Korovkin type theorems are stated and proved in these spaces. In the fourth and last part, Korovkin type approximation theorems are stated and proved in these three spaces respectively by applying the power series method, which is stronger than classical convergence, to the positive linear operator. Moreover, in each space, some examples are given to show that these newly given and proved Korovkin type theorems are stronger than the Korovkin type theorems expressed with the help of classical convergence. Finally, the rate of convergence is calculated by applying the power series method to the positive linear operator using the modulus of continuity.