The Bézier variant of Kantorovitch operators
The author introduces the following generalized Kantorovich-type operator \[ B_n(f, x)=n\sum_{k=1}^\infty p_{n,k}(x)\int_{I_k}f(t)dt, \] where \[ I_k=[k/n, (k+1)/n] \] and \[ p_{n,k}(x)=(-1)^k\frac{x^k}{k!}\phi_n^{(k)}(x). \] Here \(\phi_n(x)\) is a scalar function, which for special values reduces the operator \(B_n(f, x)\) to the well-known Szasz-Kantorovich operators and Baskakov-Kantorovich operators. Estimates for the rate of convergence of the Bezier variant of these generalized operators are derived for bounded variation functions.
scientific article; zbMATH DE number 2075454