We extend results given by Zó and Cuenya in 2007 about a general approach to problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials of some degree. This approach is called best local approximation. We consider a weighted local approximation of a vector-valued function on the origin and a weighted best local approximation of a real-valued function on several points, similar to classical problems in best local approximation with balanced neighborhood.
"Best Local Weighted Approximation. An Approach with Abstract Seminorms." Real Anal. Exchange 45 (2) 265 - 282, 2020. https://doi.org/10.14321/realanalexch.45.2.0265