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

Abstract

Abstract 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.

Keywords

• α-Bernstein operators
• Korovkin’s theorem
• α-Bernstein–Kantorovich operators
• Modulus of continuity
• Rate of convergence