Korovkin-type theorems and approximation by positive linear operators

In this thesis, Korovkin type theorems for linear positive operator sequences on Korovkin subsets and Korovkin subspaces are investigated. For this purpose, firstly, Korovkin type theorems characterizing Korovkin subspaces are given for linear positive operator sequences defined in C(X) space in the special case where X is a compact metric space (and hence C_0 (X)=C(X)). For the identity operator on C(X), Korovkin subsets were characterized. Korovkin-Type theorems in weighted continuous function spaces and L^p (X,μ ̃ )-spaces are investigated. By using the Korovkin-type theorems on spaces of continuous functions, some results are obtained for L^p (X,μ ̃ )-spaces, 1≤p<+∞. The connections between Korovkin type theorems and Stone-Weierstrass theorems were examined. Some Korovkin type theorems are given for a class of linear positive projections.