The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-2-2,
author = {Vugar E. Ismailov},
title = {On the approximation by compositions of fixed multivariate functions with univariate functions},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {117-126},
zbl = {1135.41009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-2-2}
}
Vugar E. Ismailov. On the approximation by compositions of fixed multivariate functions with univariate functions. Studia Mathematica, Tome 178 (2007) pp. 117-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-2-2/