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By means of construction of suitable functions and the method of Bojanic-Cheng, the author gives the rate of convergence of a new generalized Bernstein-Kantorovich operators for some absolutely continuous functions.

In this paper, the author introduce a class of modified Lupas-Kantorovich type operators which preserve constant and linear functions. By using modulus of continuity, modulus of smooth, K-functional and lipschitz class, the rate of convergence of these operators are derived. Finally, the author present a voronovskaya-type asymptotic formula.

In this paper, we introduce a new type λ-Bernstein operators with parameter λ∈[−1,1], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of Bn,λ(f;x) to f(x), and we see that in some cases the errors are smaller than Bn(f) to f. [ABSTRACT FROM AUTHOR]