The summability process introduced by Bell (Proc Am Math Soc 38: 548–552, 1973) is a more general and also weaker method than ordinary convergence. Recent studies have demonstrated that using this convergence in classical approximation theory provides many advantages. In this paper, we study the summability process to approximate a function and its derivatives by means of a wider class of linear operators than a family of positive linear operators. Our results improve not only Baskakov’s idea in (Mat Zametki 13: 785 794, 1973) but also the Korovkin theory based on positive linear operators. In order to verify this we display a specific sequence of approximating operators by plotting their graphs.