Statistical A-summation process and Korovkin theorem on modular spaces

In this doctoral thesis, some main definitions and theorems which were used in the study have been introduced primarily. In the first part of the findings section, Korovkin type approximation theorems have been studied with the help of B-statistical A-summation process for single sequences on modular spaces and an example which satisfies this new approximation theorem has been given. In the second part of the findings section, the concept of statistical modular convergence for double sequences has been given and Korovkin type theorems have been obtained with this concept. Then, an example that provides the condition of this theorem but does not provide for the modular Korovkin type theorem for double sequences has been given. In the last part of the findings, Korovkin type approximation theorems with the help of the statistical A-summation process for double sequences have been studied on modular spaces and an example showing that the results obtained have been stronger.