A Class of Weak Chebyshev Spaces and Characterization of Best Approximations Original Research Article

Let A ⊂ R, F(A) denote the linear space of all real functions on A. A finite-dimensional subspace U ⊂ F(A) is said to satisfy (WTr)-property if every its restriction U|A′, A′ ⊂ A, is a weak Chebyshev space. It is shown that a direct extension of the characterization of the best approximations by spline-functions holds true for every WTr-space.