Equistatistical convergence

In this thesis, we focus on di↵erent types of equistatistical convergences. We define some new type of convergences such as lacunary equistatistical convergence, !-equistatistical convergence, A-equistatistical convergence, B-equistatistical convergence and ↵#-equistatistical convergence. We also study properties of these new types of convergences. We construct examples for each case, to show that equistatistical convergence lies between point wise and uniform convergences. Moreover, we prove Korovkin type approximation theorems via lacunary equistatistical convergence, !-equistatistical convergence, A-equistatistical convergence, Bequistatistical convergence and ↵#-equistatistical convergence. In the last chapter we introduce ↵#- statistical convergence of order $ and we prove Korovkin type approximation theorems in the sense of ↵#- statistical convergence. Keywords: Statistical convergence, lacunarystatistical convergence, A-statistical convergence, !-statistical convergence, equistatistical convergence, Korovkin type approximation theorem.