Generalization of Statistical Korovkin Theorems

The classical Korovkin theory enables us to approximate a function by means of positive linear operators (see, e.g., [1– 3]). In recent years, this theory has been quite improved by some efficient tools inmathematics such as the concept of statistical convergence from summability theory, the fuzzy logic theory, the complex functions theory, the theory of q-calculus, and the theory of fractional analysis.Themain purpose of this paper is to generalize and develop this Korovkin theory by using an appropriate abstract space. Actually, the most important motivation of this study has its roots from the paper by Yoshinaga and Tamura [4]. In the present paper, we show that our new approximation is more general and also more applicable than that of [4]. Throughout the paper the following assumptions are imposed: