PHYSICS AND MATHEMATICS

On the best approximation by absolutely monotonic functions on semiaxis

V. M. Fedorov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The main result of the paper (Theorem 2) is that in the space $C(I)$ of continuous functions on the interval $I=[0,\infty]$ , the cone $K\subset C(I)$ consisting of absolutely monotone functions is Chebyshev, that is, for each continuous function $f\in C(I)$ there is a unique absolutely monotonic function $f \varphi \in K$ of the best uniform approximation on the interval $I$. In the proof, we use a special criterion for the uniqueness of the best approximation by the wedge (Theorem 1). This criterion can be used in proving the uniqueness of the best approximation for other cones consisting of continuous functions.

Keywords: best uniform approximation, reference wedge, reference plane, continuous function, absolutely monotonic function.

DOI: 10.23670/IRJ.2019.82.4.004

 English version: DOI: 10.23670/IRJ.2019.82.4.004