Many researchers have been interested in the concept of statistical convergence because of the fact that it is stronger than the classical convergence. Also, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this paper we define a new type of statistical convergence by using the notions of equi-statistical convergence and statistical equal convergence to prove a Korovkin type theorem. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. After, we present an example in support of our definition and result presented in this paper. Finally, we also compute the rates of statistical equi-equal convergence of sequences of positive linear operators.
Statistical equal convergence Equi-statistical convergence Positive linear operators Korovkin theorem Modulus of continuity
Mathematics Subject Classification
This is a preview of subscription content, log in to check access.
Acar, T., Dirik, F.: Korovkin-type theorems in weighted Lp-spaces via summation process. Sci. World J. ArticleID 534054(2013)Google Scholar
Altomare, F., Campiti, M.: Korovkin-Type Approximation Theory and Its Applications. De Gruyter Stud. Math. Walter de Gruyter, Berlin (1994)CrossRefzbMATHGoogle Scholar
Balcerzak, M., Dems, K., Komisarski, A.: Statistical convergence and ideal convergence for sequences of functions. J. Math. Anal. Appl. 328, 715–729 (2007)MathSciNetCrossRefzbMATHGoogle Scholar