Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4608311 | Journal of Approximation Theory | 2006 | 16 Pages |
Abstract
We prove an identity for basis functions of a general family of positive linear operators. It covers as special cases the Bernstein, Szász–Mirakjan and Baskakov operators. A corollary of our result can be considered a pointwise orthogonality relation. The Bernstein case is the univariate case of a remarkable identity which recently was presented by Jetter and Stöckler. As an application we give a representation of a restricted dual basis and define a class of quasi-interpolants.
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