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Abstract

Let $Q$ be a compact subset of the $d$-dimensional Euclidean space, and $C(Q)$ be the space of continuous real-valued functions on $Q$. We consider the problem of approximation of a function $f\in C(Q)$ by superpositions of the form $g\circ s+h\circ p$, where $s$, $p$ are fixed functions from $C(Q)$ and $g$, $h$ are variable univariate functions. We obtain a Chebyshev-type criterion for a function $g_{0}\circ s+h_{0}\circ p$ to be a best approximation to $f$.