Ministry of Science and Education Republic of Azerbaijan

Institute of Mathematics and Mechanics

14/09/2023

A paper coauthored by prof. Vugar Ismailov – head of the department of “Function Theory”, Aida Asgarova (PhD) – researcher of the department of “Function Theory”, and Ali Huseynli (PhD) – senior researcher of the department of “Non-Harmonic Analysis” was published in “Proceedings of the Edinburgh Mathematical Society”, a prestigious and one of the oldest (since 1884) mathematical journals in the world. “Proceedings of the Edinburgh Mathematical Society” is a journal of Edinburgh Mathematical Society (founded in 1883) and is published by “Cambridge University Press”.

In the work a Chebyshev type alternation problem for best approximation by a sum of two closed subalgebras of the space of real-valued continuous functions defined on a compact metric space is investigated.

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. The problem of approximation of a function f ∈ C(X) by elements from A_{1}+A_{2} is considered. We prove a Chebyshev type alternation theorem for a function u_{0} ∈ A_{1}+A_{2} to be a best approximation to f.

(see https://doi.org/10.1017/S0013091523000494)

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