Statistical epi-convergence

The thesis consists of seven chapters. The first chapter includes the historical development of the basic concepts related to the thesis topic and the results. In the second chapter, definitions, theorems and lemmas are given for the topics studied in the thesis. In the third chapter, statistical epi-convergence is defined and explained with examples. The relationship of this type of convergence with level sets and the case of monotony of functions are examined. In the last part of this chapter, the requirements for the overlap of statistical epi-convergence and statistical pointwise convergence are expressed. In the fourth chapter, the basic features of statistical epi-convergence are studied. In the fifth chapter, various definitions related to statistical convergence of sequence of sets are obtained by using open and closed sets and transferred to epigraphs and epi-limits. In the sixth chapter, sequential characterizations for statistical epi-convergence have been focused on. In the last chapter, the applications that show the contribution of the characterizations and theorems obtained in the previous chapter to the solutions of optimization problems are included.