TITLE:
On the Uniform and Simultaneous Approximations of Functions
AUTHORS:
Mansour Alyazidi
KEYWORDS:
Simultaneous Approximation, Uniform Approximation, Relation, Straddle Points, Alternation
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.10,
October
13,
2021
ABSTRACT: We consider the relation between the simultaneous approximation of two functions and the uniform approximation to one of these functions. In particular, F1 and F2 are continuous functions on a closed interval [a,b], S is an n-dimensional Chebyshev subspace of C[a,b]and s1* & s2* are the best uniform approximations to F1 and F2 from S respectively. The characterization of the best approximation solution is used to show that, under some restrictions on the point set of alternations of F1−s1* and F2−s2*, s1*or s2* is also a best A(1) simultaneous approximation to F1 and F2 from S with F1≥F2and n=2.