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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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