On the approximation by compositions of fixed multivariate functions with univariate functions
Tom 183 / 2007
Studia Mathematica 183 (2007), 117-126
MSC: 41A30, 41A50, 41A65.
DOI: 10.4064/sm183-2-2
Streszczenie
The approximation in the uniform norm of a continuous function $f(\mathbf{x} )=f(x_{1},\ldots,x_{n})$ by continuous sums $g_{1}( h_{1}(\mathbf{x} )) +g_{2}( h_{2}(\mathbf{x})) $, where the functions $h_{1}$ and $h_{2}$ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions $h_{1}$ and $h_{2}$.