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Area of Bernstein-type polynomials

Author: Martin E. Price
Journal: Proc. Amer. Math. Soc. 42 (1974), 222-227
MSC: Primary 41A10; Secondary 26A63
MathSciNet review: 0326236
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Abstract: Bernstein polynomials in one variable are known to be total-variation diminishing when compared to the approximated function f. Here we consider the two variable case and give a counterexample to show they are not area-diminishing. Sufficient conditions are then given on a continuous function f to insure convergence in area. A similar theorem is proved for Kantorovitch polynomials in the case f is summable.

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Keywords: Generalized area, generalized absolute continuity, Kantorovitch polynomials, Bernstein polynomials
Article copyright: © Copyright 1974 American Mathematical Society

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