Area of Bernstein-type polynomials
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- by Martin E. Price PDF
- Proc. Amer. Math. Soc. 42 (1974), 222-227 Request permission
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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 222-227
- MSC: Primary 41A10; Secondary 26A63
- DOI: https://doi.org/10.1090/S0002-9939-1974-0326236-0
- MathSciNet review: 0326236