Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

On simultaneous Chebyshev approximation in the ``sum'' norm


Author: William H. Ling
Journal: Proc. Amer. Math. Soc. 48 (1975), 185-188
MSC: Primary 41A30; Secondary 41A50
MathSciNet review: 0361555
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {f_1},{f_2}$ be real valued functions on $ [a,b]$ and let $ S$ be a nonempty family of real valued functions on $ [a,b]$. It is shown that the simultaneous approximation of $ {f_1}$ and $ {f_2}$ in the ``sum'' norm by elements of $ S$ is, with one restriction, equivalent to the approximation of the arithmetic mean, $ ({f_1} + {f_2})/2$. A complete characterization of best approximations in the ``sum'' norm is given including results for varisolvent families.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A30, 41A50

Retrieve articles in all journals with MSC: 41A30, 41A50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0361555-4
Keywords: Simultaneous approximation, "sum'' norm, best approximation, arithmetic mean, varisolvent family
Article copyright: © Copyright 1975 American Mathematical Society