# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## 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 $h_{2}$.

#### Autorzy

• Vugar E. IsmailovMathematics and Mechanics Institute