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.
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.
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