Abstract
In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals.
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Supported by Zhejiang Provincial Science Foundation.
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Zhenqiu, Z. On weighted approximation by Bernstein-Durrmeyer operators. Approx. Theory & its Appl. 7, 51–64 (1991). https://doi.org/10.1007/BF02845191
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DOI: https://doi.org/10.1007/BF02845191