Abstract: A quantitative Bohman-Korovkin type theorem is established for continuous normed-space-valued functions defined on compact convex subsets, and sequences of operators which are dominated by positive operators. A qualitative result on Korovkin systems is established for sequences of linear operators which are monotonically regular, i.e., sequences {T} such that for some sequence of positive linear operators (Sn) we have Tn(gv) = Sn(g) v, for every continuous real-valued function g and every vector v Ver menos