Korovkin type approximation theorems via statistical A-summability

This thesis consists of five chapters. First, basic definitions and the classical Korovkin theorem are given. The concept of density, the definitions and theorems of statistical convergence are stated, and the Korovkin type approximation theorem for statistical convergence, which is stronger than convergence, and the convergence rate of the statistical Korovkin type approximation theorem is given using the continuity module and the example showing that the theorem is stronger. Then, A-statistical convergence, which is an extension of statistical convergence, is introduced and the Korovkin type approximation theorem for A-statistical convergence is given. Then A-summability is introduced and the connection between A-summability, statistical A-summability and statistical convergence is mentioned. Also, the Korovkin type approximation theorem with the help of statistical A-summability and the rate of convergence of the Korovkin type approximation theorem with the help of statistical A-summability using the modulus of continuity are given. In the fifth and last section, sequences with even indices are introduced and similarly, Korovkin type approximation theorems for sequences with even indices are analyzed and examples are given. In addition, the Korovkin type approximation theorem is given with the help of statistical A-summability and the convergence rate of the obtained approximation is analyzed with the continuity modulus.