This article presents a study on the King-type modification of Bernstein–Durrmeyer-type operators introduced by Páltănea [25]. For the new King-type operators, we estimate the moments, convergence rate for continuous functions and establish a Korovkin-type theorem and a Voronovskaya-type theorem to demonstrate uniform and pointwise convergence. Moreover, we also provide an interval in which the order of approximation of the new King-type operators is better than the Páltănea operators. The Ditzian–Totik modulus of continuity and the classical modulus of continuity are used to prove quantitative convergence theorems.
