Several modifications of the discrete operators are available in the literature. In the recent years, certain modifications of the well-known Baskakov and Szász--Mirakyan operators have been discussed based on certain parameters. We propose mixed summation-integral type operators and estimate the quantitative asymptotic formula and a global direct result for the special case. For general case, we establish moments and some direct convergence results in ordinary approximation, which includes pointwise approximation, asymptotic formula and a direct result in terms of modulus of continuity.