Approximation by a new kind of \((\lambda ,\mu )\)-Bernstein–Kantorovich operators

In this manuscript, a new family of ( \(\lambda \) $\lambda$ , \(\mu \) $\mu$ )-Bernstein–Kantorovich operators are introduced. A Kovovkin type approximation theorem is obtained, the rate of convergence and A-statistical convergence are investigated by using the modulus of smoothness, Steklov mean and Korovkin-type statistical approximation theorem, graphical representations and numerical examples are also presented to compare the newly defined ones with other forms. Finally, an asymptotic estimate on the rate of convergence for some absolutely continuous functions are derived by using the Bojainc–Cheng decomposition method and some analysis techniques.