Existence of Best Rational L∝ Approximation

Abstract:

      Let R_ｆ(p)∈R_n^m[a,b] be the best rationaI L_p approximation of functionf, and let E_ｆ(p)=‖f-R_ｆ(p)‖_p.It is shown that E_ｆ(p)/(b-a)^(1/p) is an increasing andbounded function of p. If f ∈L_∞[a,b], then the best rational L_∞ approximation of fexists