Approximation properties by shifted knots type of α-Bernstein–Kantorovich–Stancu operators

Through the real polynomials of the shifted knots, the α-Bernstein–Kantorovich operators are studied in their Stancu form, and the approximation properties are obtained. We obtain some direct approximation theorem in terms of Lipschitz type maximum function and Peetre’s K-functional, as well as Korovkin’s theorem. Eventually, the modulus of continuity is used to compute the upper bound error estimation.