Korovkin type approximation theory is concerned with the convergence of the sequences of positive linear operators to the identity operator. In this paper, we deal with the Korovkin type approximation properties of the Cheney–Sharma operators by using A-statistical convergence and Abel convergence that are some well known methods of summability theory. We also study the rate of convergence. Finally, we show that the results obtained in this paper are stronger than previous ones and we support our results with particular examples and graphs.