Approximation Properties of Generalized λ -Bernstein–Stancu-Type Operators - Cai, Qing-Bo; Torun, Gülten; Dinlemez Kantar, Ülkü (Wiley, 2021)
The present study introduces generalized λ -Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of G m , λ α , β f , x to f x with respect to m values.
Keywords: QA1-939; Approximation by positive operators; Approximation by operators (in particular, by integral operators); Rate of convergence, degree of approximation; Mathematics; 16. Peace & justice