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arXiv · 2204.07448

A Chebyshev type alternation theorem for best approximation by a sum of two algebras

Aida Asgarova·Ali Huseynli·Vugar Ismailov
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Abstract

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 $f$.

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Aida Asgarova, Ali Huseynli, Vugar Ismailov. 2022-04-15. A Chebyshev type alternation theorem for best approximation by a sum of two algebras. https://doi.org/10.1017/s0013091523000494

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