The Stancu-type generalization of Jakimovski-Leviatan operators, involving confluent Appell polynomials, and their approximation features are the focus of this paper. Moreover, the modulus of continuity and Peetre-K functional are used to determine the rate of convergence of the confluent Jakimovski-Leviatan operators. Next, we demonstrate that the newly created operators diminish confluent Bernoulli polynomials and confluent Hermite polynomials, under specific choices of A(?). Lastly, we provide a graphic comparison between the newly created operators and the Stancu-type Jakimovski-Leviatan operators.
Kanat et al. (Wed,) studied this question.