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A Chebyshev-type alternation theorem for best approximation by a sum of two algebras
Published online by Cambridge University Press: 01 September 2023
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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 4 , November 2023 , pp. 971 - 978
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.