CONVEX APPROXIMATION BY RATIONAL FUNCTIONS

In this paper, the convex approximation to \x\ and to convex functions with continuous derivatives are investigated. In the first case, the approximation order c(1)e-(c2 root n) is achieved by using H-infinity quadrature. In the second case, the estimate \f(x) - R(n)(x)\less than or equal to C 1/n(2-epsilon) is proved, where is an element of is any positive real number.