APPROXIMATION, BY RATIONAL FUNCTIONS, OF CONVEX FUNCTIONS WITH GIVEN MODULUS OF CONTINUITY

Abstract

We denote by the least deviation of the continuous function , , from the rational functions of order at most .We establish the following theorems.Theorem 1. Let be convex on () with modulus of continuity . Then where is an absolute constant.Theorem 2. There exist a convex function and a sequence such that 1) , , and 2) , where is an absolute constant.Bibliography: 8 titles.