Monotone $L_ 1$-approximation on the unit $n$-cube
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- by Richard B. Darst and Robert Huotari PDF
- Proc. Amer. Math. Soc. 95 (1985), 425-428 Request permission
Abstract:
Let $\Omega$ be the unit $n$-cube ${[0,1]^n}$, and let $M$ be the set of all real-valued functions on $\Omega$, each of which is nondecreasing in each variable separately. If $f:\Omega \to \mathbb {R}$ is continuous, we show that there exists an (essentially) unique, best ${L_1}$-approximation, ${f_1}$, to $f$ by elements of $M$, and that ${f_1}$ is continuous.References
- Richard B. Darst and Robert Huotari, Best $L_1$-approximation of bounded, approximately continuous functions on $[0,1]$ by nondecreasing functions, J. Approx. Theory 43 (1985), no. 2, 178–189. MR 775785, DOI 10.1016/0021-9045(85)90125-X
- D. Landers and L. Rogge, Natural choice of $L_{1}$-approximants, J. Approx. Theory 33 (1981), no. 3, 268–280. MR 647853, DOI 10.1016/0021-9045(81)90076-9
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 425-428
- MSC: Primary 41A52; Secondary 41A29
- DOI: https://doi.org/10.1090/S0002-9939-1985-0806081-7
- MathSciNet review: 806081