1 results
A Chebyshev-type alternation theorem for best approximation by a sum of two algebras
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 4 / November 2023
- Published online by Cambridge University Press:
- 01 September 2023, pp. 971-978
-
- Article
-
- You have access
- HTML
- Export citation
-
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.
