Weighted approximation: Korovkin and quantitative type theorems

In the present paper, we consider Korovkin and quantitative theorems, which have been treated by various authors to date, under weighted approximation. After giving the basic definitions and some of well-known spaces, we mention the main theorems and their applications to linear positive operators, which have been specially treated by the authors. Therefore, this study which can be considered as a survey study will direct the readers to literature information. Furthermore, we give a general operator including well-known operators as an application of some theorems given at the end of the paper.