Durrmeyer variant of certain approximation operators (Q6586157)

New approximating positive operators are constructed on the basis of some known method of Durrmeyer. The convergence theorems for the introduced new operators, including an analogous to Korovkin's theorems, in the space of continuous and bounded on \(0,\infty\) functions, are obtained. The moment-generating function and moments of these operators via the Lambert function are estimated and some direct results are established. Moreover, a composition of these operators with Szász-Mirakjan operators are studied. A graphical comparison of their approximation properties are provided.