Derivatives of multidimensional Bernstein operators and smoothness |
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| Authors: | Feilong Cao |
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| Institution: | Department of Information and Mathematics Sciences, College of Science, China Jiliang University, Hangzhou 310018, PR China |
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| Abstract: | We characterize the directional derivatives of multidimensional Bernstein operators by a new measure of smoothness. This task is carried out by means of establishing the relation between the asymptotic behavior of the derivatives and the smoothness of the functions they approximate. The obtained results generalize the corresponding ones for univariate Bernstein operators. |
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| Keywords: | Simplex Bernstein operators Derivatives Modulus of smoothness |
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