Statistical relative convergence and korovkin type theorems on modular spaces

In this doctoral thesis, the concepts of relative modular convergence, statistical relative modular convergence and relative summation process have been used. Firstly, some main definitions and theorems used in the thesis have been given. In the first part of the findings section, the concept of relative modular convergence has been presented and via this type of convergence, Korovkin type approximation theorem has been studied on modular spaces. Then, an example, showing that the result obtained has been stronger, is given. In the second part, using statistical relative modular convergence, a Korovkin type approximation theorem has been obtained on modular spaces. Also, an example which satisfies the conditions of this theorem but does not provide the conditions of the modular and statistical modular Korovkin type theorems, given previously, has been presented. In the last part of the findings section, with the help of relative summation process, statistical Korovkin type approximation theorems have been studied on modular spaces and an example satisfying this new type approximation has been given.