Statistical relative uniform convergence and Korovkin type theorems

In this doctoral thesis, the concepts of A-statistical relative uniform convergence and statistical relative equal convergence have been used. In this thesis, firstly some definitions and theorems used in the thesis have been given. In the first part of the findings section, the concept of A-statistical relative uniform convergence has been presented for double sequences and via this type of convergence, Korovkin type approximation theorem has been studied. Then, an example, showing that the result obtained has been stronger than uniform convergence and statistical uniform convergence, is given. Finally the rate of A-statistical relative uniform convergence for this theorem has been computed. In the second part, introducing statistical relative equal convergence, a Korovkin type approximation theorem has been obtained via this type of definition. Also, an example which satisfies the conditions of this theorem but does not provide the conditions of the statistical relative Korovkin type theorems, given previously, has been presented. Then, the rate of statistical relative equal convergence has been computed. In the last part of the findings section, for double sequences the concept of statistical relative equal convergence and Korovkin type approximation theorem have been given. After then, an example satisfying this new type approximation has been studied. Finally the rate of statistical relative equal convergence for this theorem has been computed. Also, Voronovskaya type theorem has been studied.