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Published online by Cambridge University Press: 01 September 2023
Let X be a compact metric space, C(X) be the space of continuous real-valued functions on X and $A_{1},A_{2}$ be two closed subalgebras of C(X) containing constant functions. We consider the problem of approximation of a function
$f\in C(X)$ by elements from
$A_{1}+A_{2}$. We prove a Chebyshev-type alternation theorem for a function
$u_{0} \in A_{1}+A_{2}$ to be a best approximation to f.