On the approximation by compositions of fixed multivariate functions with univariate functions

The approximation in the uniform norm of a continuous function f (x) = f (x(1), ... , x(n)) by continuous sums g(1) (h(1) (x)) + g(2) (h(2) (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).