In this paper, we introduce a new type λ-Bernstein operators with parameter , 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 to , and we see that in some cases the errors are smaller than to f.

Abstract. In this paper the pointwise approximation of the Bézier variant of Chlodowsky operators for bounded variation functions is studied. By means of the analysis techniques and some results of probability theory, we obtain an estimate formula on this type approximation. Mathematics subject classification (2010): 41A36, 41A25, 41A10.

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By using Bojanic-Cheng's method and analysis techniques, the authors study the rate of convergence of Lupas-Durrmeyer type operators for some absolutely continuous functions having a derivative equivalent to a bounded variation.

Abstract. 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.

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.

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