Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On strong unicity of $L_{1}$-approximation
HTML articles powered by AMS MathViewer

by András Kroó PDF
Proc. Amer. Math. Soc. 83 (1981), 725-729 Request permission

Abstract:

Let ${C_1}$ be the space of continuous functions on $[0,1]$ with norm $\left \| f \right \| = \int _0^1 {|f(x)|} dx$, and let $G \subset {C_1}$ be a finite dimensional unicity subspace, i.e. any $f \in {C_1}$ possesses a unique best approximation out of $G$. Consider an arbitrary $f \in {C_1}$ such that 0 is its best approximation. Then for any $0 < \delta < {\delta _0}$ and $\tilde g \in G$ with $\left \| {f - \tilde g} \right \| \leqslant \left \| f \right \| + \delta$ it follows that $\left \| {\tilde g} \right \| \leqslant Kw_f^* (\delta )$, where $w_f^*(h) = {(w_f^{ - 1}(h)h)^{ - 1}}$ and ${w_f}(h)$ denotes the modulus of continuity of $f$. ($- 1$ is used to denote the inverse function.)
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A52
  • Retrieve articles in all journals with MSC: 41A52
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 725-729
  • MSC: Primary 41A52
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0630044-4
  • MathSciNet review: 630044